The large amplitude force vibrations of steel thin-walled silos when empty are investigated. The ... more The large amplitude force vibrations of steel thin-walled silos when empty are investigated. The basic geometric con…guration modeled is a cylinder clamped at the bottom with a top conical roof. Wind pressure distributions are assumed as non-axisymmetric in the circumferential direction and with a rectangular impulse or step distribution in time. Instability is identi…ed from …nite element computations of the time response of the shell using a criterion due to Budianski and Roth. Results are computed for silos made with plain as well as with corrugated sheets, and the in ‡uences of geometric imperfections and the sti¤ening due to the roof are included in the analysis. The problems are also modeled with static pressures using both continuation techniques and bifurcation analysis from a linear fundamental path. Additional results have been obtained to estimate the dynamic buckling load for step loading using energy procedures. All results are computed using …nite element codes developed by the authors.
The nonlinear dynamic response and buckling of a simple, two degree of freedom system is investig... more The nonlinear dynamic response and buckling of a simple, two degree of freedom system is investigated in this work under an impulsive load that simulates a nearby detonation-like explosion. The system includes force and moment springs in much the same way as membrane and bending effects develop in shell structures. The static response is first obtained to evaluate bifurcation states and nonlinear equilibrium paths including geometric imperfections. The dynamic problem is modeled using Lagrange equation of motion. The nonlinear dynamic response under impulsive load is next computed for the perfect configuration under increasing load levels. The presence of quasi-bifurcations is detected using stability coefficients based on second order derivatives of the total potential energy. For a given load level, it is found that one stability coefficient vanishes at the first maximum in the displacement versus time trajectory, at which the system passes through a state of zero velocity. This o...
The nonlinear dynamic response and buckling of a simple, two degree of freedom system is investig... more The nonlinear dynamic response and buckling of a simple, two degree of freedom system is investigated in this work under an impulsive load that simulates a nearby detonation-like explosion. The model considered in this work was originally studied by other researchers to explore static buckling. The system includes force and moment springs in much the same way as membrane and bending effects develop in shell structures. The static response is first obtained to evaluate bifurcation states and nonlinear equilibrium paths including geometric imperfections. The dynamic problem is modeled using Lagrange equation of motion involving the total potential and kinetic energies. The nonlinear dynamic response under impulsive load is next computed for the perfect configuration under increasing load levels. The presence of quasi-bifurcations is detected using stability coefficients based on second order derivatives of the total potential energy. For a given load level, it is found that one stabil...
The localized settlement of columns in large metal industrial buildings induces out-of-plane disp... more The localized settlement of columns in large metal industrial buildings induces out-of-plane displacements of side walls of the same order as the settlement, which may affect service conditions in the building. For a structural configuration formed by frames, side-walls and wall-girts, this work reports results from testing a small-scale model together with computational modelling of the full-scale structure. Dimensional analysis was used to scale the geometry and properties from full-scale to small-scale, leading to an overall scale factor of 1:15. Differential settlements having a controlled amplitude were imposed at the central column, and displacements were monitored using mechanical devices. The computational model employed shell elements for side-walls and wall- girts. Good agreement was found between tests and computer modelling. The results at the full- scale level, indicate that, for settlements likely to occur in granular soils, the associated lateral displacements exceed ...
Research on the buckling behavior of thin walled metal tanks used in the oil industry has been pe... more Research on the buckling behavior of thin walled metal tanks used in the oil industry has been performed at the Civil Infrastructure Research Center of the University of Puerto Rico for almost 10 years. However, the mechanics of behavior is only part of the complete picture and to address the impact of hurricanes or earthquakes on the oil industry it is necessary to have an inventory of tanks in Puerto Rico, which is the subject of this paper. This research has been done using data from aerial photographs supplemented by site visits. The information obtained are the diameter, height and the type of roof. This limited data is very useful because the design of tanks is regulated by American Petroleum Institute codes and follows rather standard geometric patterns. A vulnerability assessment of a typical existing tank is presented. It was found that this tank would not be able to sustain the current seismic and hurricane wind demand from actual codes. It is suggested that the informatio...
During the construction of steel storage oil tanks, a state of stresses under wind loads is induc... more During the construction of steel storage oil tanks, a state of stresses under wind loads is induced which is not covered by the regulations. Cases of collapse of such structures during their construction occurred in Patagonia Argentina and elsewhere under moderate wind speeds, as reported in the literature. Previous numerical studies concentrated on the identification of the collapse mechanism, which was related to the loss of structural integrity due to discontinuity of the support in the circumferential direction. An increased knowledge of the fluid dynamic behavior under wind allows obtaining an improved input used in the subsequent numerical study. This paper provides new insight into the wind behavior of unanchored tanks that collapsed during their construction by wind tunnel tests to evaluate the flow pattern inside the tanks, which is an input for the subsequent numerical study. The structure is modeled using a general purpose finite element code, in which instability is eval...
This paper reports on implementations of active learning strategies carried out for the civil eng... more This paper reports on implementations of active learning strategies carried out for the civil engineering courses. Specifically, the activities are performed by students in a computersimulated environment, in which they are assigned a role and follow a mission. As a consequence of the activity, the students prepare a product (a report, drawing, or other documents) and send it to a real tutor for evaluation. Because the simulation of the environment is the most expensive part of this class of development, a story-centered approach has been followed here, in which only part of the activities are represented in the module. This approach was originally proposed by R. C. Schank and has been adapted here for engineering education, in which formal modeling and calculations are part of the expected activities. Examples are used to illustrate the implemented activities, which refer to learning about structural failures. At the beginning of the module, the students are presented with a situat...
Las trayectorias de equilibrio en problemas estaticos con no linealidades geometricas severas pue... more Las trayectorias de equilibrio en problemas estaticos con no linealidades geometricas severas pueden presentar inestabilidades locales o globales. Una estrategia de analisis consiste en evaluar cargas criticas y modos de pandeo mediante Analisis de Bifurcacion Lineal (LBA) complementado con un Analisis No Lineal Geometrico con Imperfecciones (GNIA) implementado por metodos de longitud de arco (Riks). Esta metodologia es muy utilizada para estudiar inestabilidad del equilibrio bajo cargas de viento. Trabajos recientes han estudiado el pandeo de tanques de almacenamiento de petroleo y derivados por accion de un campo termico con metodologias numericas que utilizan un amortiguamiento artificial para tratar inestabilidades locales (ADM). En este trabajo se comparan ambos metodos para evaluar inestabilidad del equilibrio de tanques de almacenamiento de fluidos por accion de un campo termico. Se simula el comportamiento de dos tanques metalicos con techo conico donde uno de ellos esta en ...
The goal of this research is to identify what topics and procedures should be taught to engineeri... more The goal of this research is to identify what topics and procedures should be taught to engineering students in order to help them work in the field of analysis of structural failures. To identify knowledge and procedures, structured, face-to-face interviews were conducted to expert engineers, with emphasis on their methodology of research and their thinking about causes of failure. The list of questions was divided into: (a) General questions about the relation between the expert and her work; (b) Questions about a specific case in which the expert was involved; (c) Questions about the methodology used in this investigation; and (d) Questions about the development of failure hypothesis in this case. One of the future outcomes expected from this research is the creation of educational tools in which the students can do and experience in a simulated environment.
The static and dynamic behavior of a horizontal cylindrical shell (as used to store fuels in tank... more The static and dynamic behavior of a horizontal cylindrical shell (as used to store fuels in tanks) is investigated in this work by means of computational modeling. Under a distributed pressure commonly used to model effects due to explosions, the geometrically nonlinear behavior is explored to identify bifurcation and limit points along the static equilibrium path, and the associated displacements. Critical load reductions due to imperfections are found in the order of 25%. The dynamic analysis is next presented to identify the possibility of reaching a quasi-bifurcation. It is found that the first peak in the transient response at which the displacement reaches the same value as in the limit static case occurs for a load which is about 3.5 times the static bifurcation load. The velocity is zero at this state and is identified as a quasi-bifurcation, at which the shell is expected to display a static instability. Imperfection-sensitivity of the quasi-bifurcation load is found to be...
Tanques cilindricos horizontales son usados en la industria del petroleo para almacenar combustib... more Tanques cilindricos horizontales son usados en la industria del petroleo para almacenar combustible, agua o fluidos producto de las operaciones de produccion de petroleo. Estos tanques atmosfericos generalmente son construidos en acero y estan montados sobre apoyos de tipo cuna o silla de montar en dos o tres puntos. Si bien existen codigos aplicables a su diseno, en muchos casos son construidos en talleres en base a experiencia propia presentandose posteriormente danos con riesgos de perdidas de fluido y posible contaminacion ambiental. Hay escasas contribuciones sobre el tema en la literatura tecnica. En este trabajo se pretende caracterizar los modos de falla de esta tipologia de tanques horizontales frente a solicitaciones de presion hidrostatica combinada con vacio interior por operaciones de descarga y/o por asentamientos diferenciales de apoyo. Estos tanques son de menor tamano que los verticales y se han observado formas de falla de caracteristicas diferentes respecto a los ...
Latin American Journal of Solids and Structures, 2016
Micro-buckling of unidirectional fiber-reinforced composites is investigated in this paper by mea... more Micro-buckling of unidirectional fiber-reinforced composites is investigated in this paper by means of an explicit representation of a geometrically imperfect fiber within the context of kinematical and material non-linear behavior. Two types of fiber imperfections are considered: a helicoidal shape, identified as 3D imperfection; and a sinusoidal plane shape (2D imperfection). Both imperfection models are characterized by a maximum misalignment angle of the fiber with respect to the ideal or perfect configuration, as is usually considered in this field. A total of 816 cases were computed in terms of imperfection type (either 2D or 3D), fiber volume fraction, fiber arrangement (square or hexagonal array), orientation for 2D models, matrix yield stress, and misalignment angle. Two load cases, with constrained and unconstrained transverse strain, were considered. Assuming periodic boundary conditions, homogenization was carried out to obtain macroscopic stresses. Numerical results are compared with an analytical model available in the literature. The results show a high imperfection-sensitivity for small misalignment angles; on the other hand, the type of imperfection and the fiber arrangement do not have a large influence on the results. In addition, it was found that this problem is governed by fiber volume fraction and matrix yield stress only for small imperfections, whereas for large misalignment angles, a change in fiber volume fraction produces small changes in micro-buckling stress.
This paper considers the buckling and post-buckling behavior of empty metal storage tanks under w... more This paper considers the buckling and post-buckling behavior of empty metal storage tanks under wind load. The structures of such tanks may be idealized as cantilever cylindrical shells, and the structural response is investigated using a computational model. The modeling employs a doubly curved finite element based on a theory by Simo and coworkers, which is capable of handling large displacements and plasticity. Buckling results for tanks with four different geometric relations are presented to consider the influence of the ratios between the radius and the height of the shell (R/L), and between the radius and the thickness (R/t). The studies aim to clarify the differences in the shells regarding their imperfection-sensitivity. The results show that thin-walled short tanks, with R/L = 3, display high imperfection sensitivity, while tanks with R/L = 0.5 are almost insensitive to imperfections. Changes in the total potential energy of tanks that would buckle under the same high wind pressures are also considered.
Latin American Journal of Solids and Structures, 2016
This paper presents an analytical solution to predict the nonlinear forced vibrations of elastic ... more This paper presents an analytical solution to predict the nonlinear forced vibrations of elastic thin-walled cylindrical shells under suddenly applied loads. Interest in this problem is motivated by effects due to explosions on fluid-storage metal tanks. The model is based on the energy criterion due to Lagrange, in which the kinematic nonlinear relations are assumed using Donnell's simplified shell theory. Solution is achieved as a series summation in terms of trigonometric functions in the axial and circumferential directions, whereas the degrees of freedom depend on time. A blast load is assumed to represent effects due to explosions on the shell as timedependent pressures with a given circumferential distribution (a cosine square distribution in terms of the central angle). The procedure is validated by comparison with a nonlinear finite element model under the same load conditions. The influence of load level and shell geometry on the transient response is investigated by mean of parametric studies. Good accuracy is found in the results for the range of shells which are representative of horizontal, fuel storage tanks in the oil industry.
Shell buckling problems belong to the class of geometrically nonlinear behavior, and may be coupl... more Shell buckling problems belong to the class of geometrically nonlinear behavior, and may be coupled with material nonlinearity of the shell. There are many general-purpose finite element programs that perform geometric and material nonlinear analysis of shells; however, this does not mean that a user can feed data and collect reliable results without a full understanding of the physics of the problem. This paper discusses the theories involved in the explanation and classification of phenomena, and in the prediction of results. Next, those approaches are considered in the practical analysis of one shell form, namely thin-walled steel tanks used to store oil. Results have been obtained with the general-purpose package ABAQUS, and they tend to show that their interpretation requires the use of Koiter's theory in order to make sense of what is obtained. Some thoughts on possible ways to implement Croll's lower bound reduced energy approach in practice are given.
A strategy, known as Reduced Stiffness (or Reduced Energy) Method, in which selected energy compo... more A strategy, known as Reduced Stiffness (or Reduced Energy) Method, in which selected energy components are eliminated from the analysis to account for mode interaction and imperfection-sensitivity in a simplified way, has been developed by Croll and co-workers since the 1980s. This physical interpretation allows the formulation as an eigenvalue problem, in which the critical loads are lower bounds to experiments and to nonlinear incremental analysis. This paper considers the computational implementation of both reduced stiffness and reduced energy approaches to the buckling of shell structures. The structural configurations of interest in this work are cylindrical storage tanks with or without a roof. The reduced stiffness approach has been implemented in a special purpose finite element code for shells of revolution, while the reduced energy methodology was implemented in a general purpose code. The present results are compared with geometrically nonlinear analysis including shape imperfections. Links between this methodology and the Reduced Integration Technique employed in the analysis of plates/shells are discussed. Difficulties in extending the methodologies to complex problems in engineering practice are highlighted.
En este trabajo se utiliza el método de elementos finitos para estudiar el comportamiento de estr... more En este trabajo se utiliza el método de elementos finitos para estudiar el comportamiento de estructuras celulares formadas por celdas hexagonales, bajo compresión en una dirección, con el fin de obtener los valores de los parámetros macroscópicos que definen a un sólido continuo equivalente. Estos parámetros se obtienen a partir de las respuestas calculadas para varias configuraciones de geometría. Estudios comparativos de diferentes configuraciones permiten identificar el tamañoóptimo de panal para obtener una adecuada caracterización macromecánica a partir de un ensayo de compresión unidimensional. Se hace un estudio de la conveniencia de utilizar un análisis lineal de autovalores o métodos de continuación.
En este trabajo se investiga una metodología de energía reducida para calcular el límite inferior... more En este trabajo se investiga una metodología de energía reducida para calcular el límite inferior de carga de pandeo de paneles cilíndricos rebajados. La formulación de esta nueva metodología está basada en los postulados establecidos en la literatura para el cálculo de límites inferiores de carga de pandeo y se ha implementado en un programa de elementos finitos de aplicaciones múltiples. Se han analizado paneles formados de material isotrópico y caracterizados por tres valores del parámetro de Batdorf. De la comparación de los resultados obtenidos con la metodología propuesta con aquellos obtenidos de análisis no lineales incluyendo diferentes niveles de imperfección geométrica, surge que el modelo de energía reducida aplicado a paneles cilíndricos no conduce a límites inferiores de carga de pandeo. Si bien este nuevo modelo de energía reducida predice cargas de pandeo inferiores a las obtenidas del análisis clásico,éstas son mayores que las obtenidas de análisis no lineales. Sin embargo, la viabilidad de la implementación de una metodología de energía reducida en un programa de elementos finitos de aplicaciones múltiples queda demostrada.
International Journal of Solids and Structures, 1997
Imperfection sensitivity of the fiber micro-buckling problem is a fundamental requirement for app... more Imperfection sensitivity of the fiber micro-buckling problem is a fundamental requirement for applying any fiber micro-buckling model for the prediction of composite compression strength. This paper is devoted to prove theoretically that fiber micro-buckling of elastic-nonlinear polymer-matrix composites is an imperfection sensitive problem. From the proof, it follows that compression strength can be predicted by a suitable model that includes fiber misalignment as the imperfection parameter. The conditions on the behavior of the constituents (fiber and matrix) for imperfection sensitivity are derived. A novel representation for the non-linear shear response of the composite is proposed and supported with experimental data. Also, arguments are presented to support the use of composite constitutive equations rather than using micro-mechanics, particularly when material non-linearity is involved.
Aboveground metal storage tanks are used in the Caribbean islands and the United States as part o... more Aboveground metal storage tanks are used in the Caribbean islands and the United States as part of the infrastructure supporting the storage and distribution of oil and fuel. To assure the continuing supply of such products, this infrastructure should be in service following major natural hazards, including earthquakes, hurricanes, and floods. This paper reports results from a five-year research program on the structural consequences of natural hazards on thin-walled metal tanks with large diameter and low aspect ratio (short tanks). The tanks considered have several roof configurations, including conical, shallow spherical cap, flat, and floating roofs. Most tanks have rafters and columns to support the roof. The emphasis of the study is on the computational modeling of the structural response to predict buckling of the shell due to external loads. In the case of wind loads, two studies were carried out to estimate pressures on the shell: First, wind tunnel experiments on small scale models; and second, computational fluid dynamics simulations. For earthquake loads, the liquid stored plays an important role in the evaluation of loads, and both hydrostatic and sloshing actions have been considered in the analysis.
The large amplitude force vibrations of steel thin-walled silos when empty are investigated. The ... more The large amplitude force vibrations of steel thin-walled silos when empty are investigated. The basic geometric con…guration modeled is a cylinder clamped at the bottom with a top conical roof. Wind pressure distributions are assumed as non-axisymmetric in the circumferential direction and with a rectangular impulse or step distribution in time. Instability is identi…ed from …nite element computations of the time response of the shell using a criterion due to Budianski and Roth. Results are computed for silos made with plain as well as with corrugated sheets, and the in ‡uences of geometric imperfections and the sti¤ening due to the roof are included in the analysis. The problems are also modeled with static pressures using both continuation techniques and bifurcation analysis from a linear fundamental path. Additional results have been obtained to estimate the dynamic buckling load for step loading using energy procedures. All results are computed using …nite element codes developed by the authors.
The nonlinear dynamic response and buckling of a simple, two degree of freedom system is investig... more The nonlinear dynamic response and buckling of a simple, two degree of freedom system is investigated in this work under an impulsive load that simulates a nearby detonation-like explosion. The system includes force and moment springs in much the same way as membrane and bending effects develop in shell structures. The static response is first obtained to evaluate bifurcation states and nonlinear equilibrium paths including geometric imperfections. The dynamic problem is modeled using Lagrange equation of motion. The nonlinear dynamic response under impulsive load is next computed for the perfect configuration under increasing load levels. The presence of quasi-bifurcations is detected using stability coefficients based on second order derivatives of the total potential energy. For a given load level, it is found that one stability coefficient vanishes at the first maximum in the displacement versus time trajectory, at which the system passes through a state of zero velocity. This o...
The nonlinear dynamic response and buckling of a simple, two degree of freedom system is investig... more The nonlinear dynamic response and buckling of a simple, two degree of freedom system is investigated in this work under an impulsive load that simulates a nearby detonation-like explosion. The model considered in this work was originally studied by other researchers to explore static buckling. The system includes force and moment springs in much the same way as membrane and bending effects develop in shell structures. The static response is first obtained to evaluate bifurcation states and nonlinear equilibrium paths including geometric imperfections. The dynamic problem is modeled using Lagrange equation of motion involving the total potential and kinetic energies. The nonlinear dynamic response under impulsive load is next computed for the perfect configuration under increasing load levels. The presence of quasi-bifurcations is detected using stability coefficients based on second order derivatives of the total potential energy. For a given load level, it is found that one stabil...
The localized settlement of columns in large metal industrial buildings induces out-of-plane disp... more The localized settlement of columns in large metal industrial buildings induces out-of-plane displacements of side walls of the same order as the settlement, which may affect service conditions in the building. For a structural configuration formed by frames, side-walls and wall-girts, this work reports results from testing a small-scale model together with computational modelling of the full-scale structure. Dimensional analysis was used to scale the geometry and properties from full-scale to small-scale, leading to an overall scale factor of 1:15. Differential settlements having a controlled amplitude were imposed at the central column, and displacements were monitored using mechanical devices. The computational model employed shell elements for side-walls and wall- girts. Good agreement was found between tests and computer modelling. The results at the full- scale level, indicate that, for settlements likely to occur in granular soils, the associated lateral displacements exceed ...
Research on the buckling behavior of thin walled metal tanks used in the oil industry has been pe... more Research on the buckling behavior of thin walled metal tanks used in the oil industry has been performed at the Civil Infrastructure Research Center of the University of Puerto Rico for almost 10 years. However, the mechanics of behavior is only part of the complete picture and to address the impact of hurricanes or earthquakes on the oil industry it is necessary to have an inventory of tanks in Puerto Rico, which is the subject of this paper. This research has been done using data from aerial photographs supplemented by site visits. The information obtained are the diameter, height and the type of roof. This limited data is very useful because the design of tanks is regulated by American Petroleum Institute codes and follows rather standard geometric patterns. A vulnerability assessment of a typical existing tank is presented. It was found that this tank would not be able to sustain the current seismic and hurricane wind demand from actual codes. It is suggested that the informatio...
During the construction of steel storage oil tanks, a state of stresses under wind loads is induc... more During the construction of steel storage oil tanks, a state of stresses under wind loads is induced which is not covered by the regulations. Cases of collapse of such structures during their construction occurred in Patagonia Argentina and elsewhere under moderate wind speeds, as reported in the literature. Previous numerical studies concentrated on the identification of the collapse mechanism, which was related to the loss of structural integrity due to discontinuity of the support in the circumferential direction. An increased knowledge of the fluid dynamic behavior under wind allows obtaining an improved input used in the subsequent numerical study. This paper provides new insight into the wind behavior of unanchored tanks that collapsed during their construction by wind tunnel tests to evaluate the flow pattern inside the tanks, which is an input for the subsequent numerical study. The structure is modeled using a general purpose finite element code, in which instability is eval...
This paper reports on implementations of active learning strategies carried out for the civil eng... more This paper reports on implementations of active learning strategies carried out for the civil engineering courses. Specifically, the activities are performed by students in a computersimulated environment, in which they are assigned a role and follow a mission. As a consequence of the activity, the students prepare a product (a report, drawing, or other documents) and send it to a real tutor for evaluation. Because the simulation of the environment is the most expensive part of this class of development, a story-centered approach has been followed here, in which only part of the activities are represented in the module. This approach was originally proposed by R. C. Schank and has been adapted here for engineering education, in which formal modeling and calculations are part of the expected activities. Examples are used to illustrate the implemented activities, which refer to learning about structural failures. At the beginning of the module, the students are presented with a situat...
Las trayectorias de equilibrio en problemas estaticos con no linealidades geometricas severas pue... more Las trayectorias de equilibrio en problemas estaticos con no linealidades geometricas severas pueden presentar inestabilidades locales o globales. Una estrategia de analisis consiste en evaluar cargas criticas y modos de pandeo mediante Analisis de Bifurcacion Lineal (LBA) complementado con un Analisis No Lineal Geometrico con Imperfecciones (GNIA) implementado por metodos de longitud de arco (Riks). Esta metodologia es muy utilizada para estudiar inestabilidad del equilibrio bajo cargas de viento. Trabajos recientes han estudiado el pandeo de tanques de almacenamiento de petroleo y derivados por accion de un campo termico con metodologias numericas que utilizan un amortiguamiento artificial para tratar inestabilidades locales (ADM). En este trabajo se comparan ambos metodos para evaluar inestabilidad del equilibrio de tanques de almacenamiento de fluidos por accion de un campo termico. Se simula el comportamiento de dos tanques metalicos con techo conico donde uno de ellos esta en ...
The goal of this research is to identify what topics and procedures should be taught to engineeri... more The goal of this research is to identify what topics and procedures should be taught to engineering students in order to help them work in the field of analysis of structural failures. To identify knowledge and procedures, structured, face-to-face interviews were conducted to expert engineers, with emphasis on their methodology of research and their thinking about causes of failure. The list of questions was divided into: (a) General questions about the relation between the expert and her work; (b) Questions about a specific case in which the expert was involved; (c) Questions about the methodology used in this investigation; and (d) Questions about the development of failure hypothesis in this case. One of the future outcomes expected from this research is the creation of educational tools in which the students can do and experience in a simulated environment.
The static and dynamic behavior of a horizontal cylindrical shell (as used to store fuels in tank... more The static and dynamic behavior of a horizontal cylindrical shell (as used to store fuels in tanks) is investigated in this work by means of computational modeling. Under a distributed pressure commonly used to model effects due to explosions, the geometrically nonlinear behavior is explored to identify bifurcation and limit points along the static equilibrium path, and the associated displacements. Critical load reductions due to imperfections are found in the order of 25%. The dynamic analysis is next presented to identify the possibility of reaching a quasi-bifurcation. It is found that the first peak in the transient response at which the displacement reaches the same value as in the limit static case occurs for a load which is about 3.5 times the static bifurcation load. The velocity is zero at this state and is identified as a quasi-bifurcation, at which the shell is expected to display a static instability. Imperfection-sensitivity of the quasi-bifurcation load is found to be...
Tanques cilindricos horizontales son usados en la industria del petroleo para almacenar combustib... more Tanques cilindricos horizontales son usados en la industria del petroleo para almacenar combustible, agua o fluidos producto de las operaciones de produccion de petroleo. Estos tanques atmosfericos generalmente son construidos en acero y estan montados sobre apoyos de tipo cuna o silla de montar en dos o tres puntos. Si bien existen codigos aplicables a su diseno, en muchos casos son construidos en talleres en base a experiencia propia presentandose posteriormente danos con riesgos de perdidas de fluido y posible contaminacion ambiental. Hay escasas contribuciones sobre el tema en la literatura tecnica. En este trabajo se pretende caracterizar los modos de falla de esta tipologia de tanques horizontales frente a solicitaciones de presion hidrostatica combinada con vacio interior por operaciones de descarga y/o por asentamientos diferenciales de apoyo. Estos tanques son de menor tamano que los verticales y se han observado formas de falla de caracteristicas diferentes respecto a los ...
Latin American Journal of Solids and Structures, 2016
Micro-buckling of unidirectional fiber-reinforced composites is investigated in this paper by mea... more Micro-buckling of unidirectional fiber-reinforced composites is investigated in this paper by means of an explicit representation of a geometrically imperfect fiber within the context of kinematical and material non-linear behavior. Two types of fiber imperfections are considered: a helicoidal shape, identified as 3D imperfection; and a sinusoidal plane shape (2D imperfection). Both imperfection models are characterized by a maximum misalignment angle of the fiber with respect to the ideal or perfect configuration, as is usually considered in this field. A total of 816 cases were computed in terms of imperfection type (either 2D or 3D), fiber volume fraction, fiber arrangement (square or hexagonal array), orientation for 2D models, matrix yield stress, and misalignment angle. Two load cases, with constrained and unconstrained transverse strain, were considered. Assuming periodic boundary conditions, homogenization was carried out to obtain macroscopic stresses. Numerical results are compared with an analytical model available in the literature. The results show a high imperfection-sensitivity for small misalignment angles; on the other hand, the type of imperfection and the fiber arrangement do not have a large influence on the results. In addition, it was found that this problem is governed by fiber volume fraction and matrix yield stress only for small imperfections, whereas for large misalignment angles, a change in fiber volume fraction produces small changes in micro-buckling stress.
This paper considers the buckling and post-buckling behavior of empty metal storage tanks under w... more This paper considers the buckling and post-buckling behavior of empty metal storage tanks under wind load. The structures of such tanks may be idealized as cantilever cylindrical shells, and the structural response is investigated using a computational model. The modeling employs a doubly curved finite element based on a theory by Simo and coworkers, which is capable of handling large displacements and plasticity. Buckling results for tanks with four different geometric relations are presented to consider the influence of the ratios between the radius and the height of the shell (R/L), and between the radius and the thickness (R/t). The studies aim to clarify the differences in the shells regarding their imperfection-sensitivity. The results show that thin-walled short tanks, with R/L = 3, display high imperfection sensitivity, while tanks with R/L = 0.5 are almost insensitive to imperfections. Changes in the total potential energy of tanks that would buckle under the same high wind pressures are also considered.
Latin American Journal of Solids and Structures, 2016
This paper presents an analytical solution to predict the nonlinear forced vibrations of elastic ... more This paper presents an analytical solution to predict the nonlinear forced vibrations of elastic thin-walled cylindrical shells under suddenly applied loads. Interest in this problem is motivated by effects due to explosions on fluid-storage metal tanks. The model is based on the energy criterion due to Lagrange, in which the kinematic nonlinear relations are assumed using Donnell's simplified shell theory. Solution is achieved as a series summation in terms of trigonometric functions in the axial and circumferential directions, whereas the degrees of freedom depend on time. A blast load is assumed to represent effects due to explosions on the shell as timedependent pressures with a given circumferential distribution (a cosine square distribution in terms of the central angle). The procedure is validated by comparison with a nonlinear finite element model under the same load conditions. The influence of load level and shell geometry on the transient response is investigated by mean of parametric studies. Good accuracy is found in the results for the range of shells which are representative of horizontal, fuel storage tanks in the oil industry.
Shell buckling problems belong to the class of geometrically nonlinear behavior, and may be coupl... more Shell buckling problems belong to the class of geometrically nonlinear behavior, and may be coupled with material nonlinearity of the shell. There are many general-purpose finite element programs that perform geometric and material nonlinear analysis of shells; however, this does not mean that a user can feed data and collect reliable results without a full understanding of the physics of the problem. This paper discusses the theories involved in the explanation and classification of phenomena, and in the prediction of results. Next, those approaches are considered in the practical analysis of one shell form, namely thin-walled steel tanks used to store oil. Results have been obtained with the general-purpose package ABAQUS, and they tend to show that their interpretation requires the use of Koiter's theory in order to make sense of what is obtained. Some thoughts on possible ways to implement Croll's lower bound reduced energy approach in practice are given.
A strategy, known as Reduced Stiffness (or Reduced Energy) Method, in which selected energy compo... more A strategy, known as Reduced Stiffness (or Reduced Energy) Method, in which selected energy components are eliminated from the analysis to account for mode interaction and imperfection-sensitivity in a simplified way, has been developed by Croll and co-workers since the 1980s. This physical interpretation allows the formulation as an eigenvalue problem, in which the critical loads are lower bounds to experiments and to nonlinear incremental analysis. This paper considers the computational implementation of both reduced stiffness and reduced energy approaches to the buckling of shell structures. The structural configurations of interest in this work are cylindrical storage tanks with or without a roof. The reduced stiffness approach has been implemented in a special purpose finite element code for shells of revolution, while the reduced energy methodology was implemented in a general purpose code. The present results are compared with geometrically nonlinear analysis including shape imperfections. Links between this methodology and the Reduced Integration Technique employed in the analysis of plates/shells are discussed. Difficulties in extending the methodologies to complex problems in engineering practice are highlighted.
En este trabajo se utiliza el método de elementos finitos para estudiar el comportamiento de estr... more En este trabajo se utiliza el método de elementos finitos para estudiar el comportamiento de estructuras celulares formadas por celdas hexagonales, bajo compresión en una dirección, con el fin de obtener los valores de los parámetros macroscópicos que definen a un sólido continuo equivalente. Estos parámetros se obtienen a partir de las respuestas calculadas para varias configuraciones de geometría. Estudios comparativos de diferentes configuraciones permiten identificar el tamañoóptimo de panal para obtener una adecuada caracterización macromecánica a partir de un ensayo de compresión unidimensional. Se hace un estudio de la conveniencia de utilizar un análisis lineal de autovalores o métodos de continuación.
En este trabajo se investiga una metodología de energía reducida para calcular el límite inferior... more En este trabajo se investiga una metodología de energía reducida para calcular el límite inferior de carga de pandeo de paneles cilíndricos rebajados. La formulación de esta nueva metodología está basada en los postulados establecidos en la literatura para el cálculo de límites inferiores de carga de pandeo y se ha implementado en un programa de elementos finitos de aplicaciones múltiples. Se han analizado paneles formados de material isotrópico y caracterizados por tres valores del parámetro de Batdorf. De la comparación de los resultados obtenidos con la metodología propuesta con aquellos obtenidos de análisis no lineales incluyendo diferentes niveles de imperfección geométrica, surge que el modelo de energía reducida aplicado a paneles cilíndricos no conduce a límites inferiores de carga de pandeo. Si bien este nuevo modelo de energía reducida predice cargas de pandeo inferiores a las obtenidas del análisis clásico,éstas son mayores que las obtenidas de análisis no lineales. Sin embargo, la viabilidad de la implementación de una metodología de energía reducida en un programa de elementos finitos de aplicaciones múltiples queda demostrada.
International Journal of Solids and Structures, 1997
Imperfection sensitivity of the fiber micro-buckling problem is a fundamental requirement for app... more Imperfection sensitivity of the fiber micro-buckling problem is a fundamental requirement for applying any fiber micro-buckling model for the prediction of composite compression strength. This paper is devoted to prove theoretically that fiber micro-buckling of elastic-nonlinear polymer-matrix composites is an imperfection sensitive problem. From the proof, it follows that compression strength can be predicted by a suitable model that includes fiber misalignment as the imperfection parameter. The conditions on the behavior of the constituents (fiber and matrix) for imperfection sensitivity are derived. A novel representation for the non-linear shear response of the composite is proposed and supported with experimental data. Also, arguments are presented to support the use of composite constitutive equations rather than using micro-mechanics, particularly when material non-linearity is involved.
Aboveground metal storage tanks are used in the Caribbean islands and the United States as part o... more Aboveground metal storage tanks are used in the Caribbean islands and the United States as part of the infrastructure supporting the storage and distribution of oil and fuel. To assure the continuing supply of such products, this infrastructure should be in service following major natural hazards, including earthquakes, hurricanes, and floods. This paper reports results from a five-year research program on the structural consequences of natural hazards on thin-walled metal tanks with large diameter and low aspect ratio (short tanks). The tanks considered have several roof configurations, including conical, shallow spherical cap, flat, and floating roofs. Most tanks have rafters and columns to support the roof. The emphasis of the study is on the computational modeling of the structural response to predict buckling of the shell due to external loads. In the case of wind loads, two studies were carried out to estimate pressures on the shell: First, wind tunnel experiments on small scale models; and second, computational fluid dynamics simulations. For earthquake loads, the liquid stored plays an important role in the evaluation of loads, and both hydrostatic and sloshing actions have been considered in the analysis.
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Papers by Luis Godoy