Based on the nonlinear dynamic analysis, thermally induced vibrations of the FGM shallow arches s... more Based on the nonlinear dynamic analysis, thermally induced vibrations of the FGM shallow arches subjected to different sudden thermal loads are studied. Temperature and position dependence of the material properties are taken into account. Based on the uncoupled thermoelasticity assumptions, The non-linear one-dimensional transient heat conduction equation is solved numerically by a hybrid iterative GDQ method and Crank-Nicolson time marching scheme. A first order shear deformation arch theory (FSDT) is also combined with the von Kármán type of geometrical non-linearity and the Donnell kinematic assumption to obtain the equations of motion employing the Hamilton principle. Discretization of the highly coupled non-linear equations of motion is done by using the GDQ method in the arch domain. The solution of the system of the ordinary differential equations is established by means of a hybrid iterative Picard-Newmark scheme. Comparison is also made with the existing results for the case of isotropic homogeneous shallow arches, where good agreement is obtained. Also, parametric studies are proposed to show the effects of temperature dependency, geometrical non-linearity, arch thickness, power law index, and the type of thermal-mechanical boundary conditions upon the arch deflection.
Computers & mathematics with applications, Mar 1, 2018
In this investigation, the asymmetrical buckling behaviour of FGM annular plates resting on parti... more In this investigation, the asymmetrical buckling behaviour of FGM annular plates resting on partial Winkler-type elastic foundation under uniform temperature elevation is investigated. Material properties of the plate are assumed to be temperature dependent. Each property of the plate is graded across the thickness direction using a power law function. First order shear deformation plate theory and von Kármán type of geometrical nonlinearity are used to obtain the equilibrium equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained considering the deflection-less conditions. Only plates which are clamped on both inner and outer edges are considered. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The governing equations are divided into two sets. The first set, which is associated with the in-contact region and the second set which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalised differential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved iteratively to obtain the critical conditions of the plate, the associated circumferential mode number and buckled shape of the plate. Benchmark results are given in tabular and graphical presentations dealing with critical buckling temperature and buckled shape of the plate. Numerical results are given to explore the effects of elastic foundation, foundation radius, plate thickness, plate hole size, and power law index of the graded plate. It is shown that, stiffness foundation, and radius of foundation may change the buckled shape of the plate in both circumferential and radial directions. Furthermore, as the stiffness of the foundation or radius of foundation increases, critical buckling temperature of the plate enhances.
Abstract Natural frequencies of a conical–spherical functionally graded material (FGM) shell are ... more Abstract Natural frequencies of a conical–spherical functionally graded material (FGM) shell are obtained in this study. It is assumed that the conical and spherical shell components have identical thickness. The system of joined shell is made from FGMs, where properties of the shell are graded through the thickness direction. The first order shear deformation theory of shells is used to investigate the effects of shear strains and rotary inertia. The Donnel type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations are discretized using the semi-analytical generalized differential quadrature (GDQ) method. Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells with the data of conventional finite element software, parametric studies are carried out for the system of combined moderately thick conical–spherical joined shells made of FGMs and various types of end supports.
The present research deals with the nonaxisymmetric buckling behaviour of isotropic homogeneous a... more The present research deals with the nonaxisymmetric buckling behaviour of isotropic homogeneous annular plates subjected to simultaneous effects of uniform temperature rise and constant angular speed. Firstorder shear deformation plate theory is used to obtain the complete set of governing equations and the associated boundary conditions. Pre-buckling deformations and stresses of the plate are obtained using the solution of a plane stress formulation, neglecting the rotations and lateral deflection. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The resulting equations are solved using a hybrid method, including the exact trigonometric functions through the circumferential direction and generalised differential quadrature method through the radial direction. The resulting eigenvalue problem is solved to obtain the critical conditions of the plate and the associated circumferential mode number. Numerical results reveal that, only for annular plates with exterior edge clamped, rotation may enhance the critical buckling temperature of a plate under special circumstances. Furthermore, asymmetric stability analysis should be performed to extract the critical state and buckled shape of a rotating annular plate subjected to uniform heating. Otherwise, the critical buckling temperature is overestimated and the buckling pattern is wrongly predicted.
Free vibration response of a joined shell system including cylindrical and spherical shells is an... more Free vibration response of a joined shell system including cylindrical and spherical shells is analyzed in this research. It is assumed that the system of joined shell is made from a functionally graded material (FGM). Properties of the shells are assumed to be graded through the thickness. Both shells are unified in thickness. To capture the effects of through-the-thickness shear deformations and rotary inertias, first-order shear deformation theory of shells is used. The Donnell type of kinematic assumptions is adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations is discretized using the semi-analytical generalized differential quadrature method. Considering the clamped and free boundary conditions for the end of the cylindrical shell and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies of the joined shell. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells, some parametric studies are carried out for the system of combined moderately thick cylindrical–spherical shell system. Novel results are provided for the case of FGM joined shells to explore the influence of power-law index and geometric properties.
Free vibration behaviour of a shear deformable conical shell with intermediate ring support is an... more Free vibration behaviour of a shear deformable conical shell with intermediate ring support is analysed in this research. It is assumed that the conical shell is made from a linearly elastic isotropic homogeneous material. To capture the through-thethickness shear deformations and rotary inertia effects, first order shear deformation theory of shells accompanied with the Donnell type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary conditions with the aid of Hamilton's principle. The resulting system of equations are discreted using the semi-analytical generalised differential quadrature (GDQ) method. The shell is divided into two sections, where the continuity conditions are satisfied at the ring position. Considering various types of boundary conditions for the shell ends and continuity conditions at the ring position, an eigenvalue problem is established to examine the natural frequencies of the shell reinforced with an intermediate ring support. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous cylindrical shell with intermediate ring support, parametric studies are carried out for the case of shear deformable conical shells with intermediate ring support.
European Journal of Computational Mechanics, Jan 16, 2019
In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate su... more In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate subjected to uniform compression on both inner and outer edges is analysed. It is further assumed that the plate is rotating with a constant angular speed. Formulation is based on the first order shear deformation plate theory, which is valid for thin and moderately thick plates. The complete set of equilibrium equations and the associated boundary conditions are obtained for the plate. Prebuckling loads of the plate are obtained under flatness and axisymmetric deformations. Using the adjacent equilibrium criterion, the linearised stability equations are extracted. An asymmetric stability analysis is performed to obtain the critical buckling loads of the plate and the buckled configurations of the rotating plate. To this end, trigonometric functions through the circumferential direction and the generalised differential quadrature discretization across the radial direction are used which result in an algebraic eigenvalue problem. Benchmark results are given in graphical presentations for combinations of free, simply-supported, sliding supported, and clamped types of boundary conditions. It is shown that rotation enhances the buckling loads of the plate for all types of boundary conditions and alters the buckled shape of the plate.
In this investigation, the asymmetrical buckling behavior of isotropic homogeneous annular plates... more In this investigation, the asymmetrical buckling behavior of isotropic homogeneous annular plates resting on a partial Winkler-type elastic foundation under uniform temperature elevation is investigated. First-order shear deformation plate theory is used to obtain the governing equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained under the solution of a plane stress formulation, neglecting the rotations and lateral de ection. Applying the adjacent equilibrium criterion, the linearized stability equations are obtained. The governing equations are divided into two sets. The rst set, which is associated with the in-contact region, and the second set, which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalized di erential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved to obtain the critical conditions of the plate and the associated circumferential mode number. Benchmark results are given in tabular and graphical presentations for combinations of simply supported and clamped types of boundary conditions. Numerical results are given to explore the e ects of elastic foundation, foundation radius, plate thickness, plate hole size, and the boundary conditions.
Free vibration analysis of a joined shell system composed of two conical shells is analysed in th... more Free vibration analysis of a joined shell system composed of two conical shells is analysed in this research. It is assumed that the system of joined shell is made from a linearly elastic isotropic homogeneous material. Both shells are unified in thickness. To capture the through-the-thickness shear deformations and rotary inertias, first order theory of shells is accompanied with the Donnell type of kinematic assumptions to establish the general motion equations and the associated boundary and continuity conditions with the aid of Hamilton's principle. The resulted system of equations are discreted using the semi-analytical generalised differential quadrature (GDQ) method. Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies as well as the associated mode shapes. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells, some parametric studies are carried out for the system of combined moderately thick conical-conical.
In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate su... more In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate subjected to uniform compression on both inner and outer edges is analysed. It is further assumed that the plate is rotating with a constant angular speed. Formulation is based on the first order shear deformation plate theory, which is valid for thin and moderately thick plates. The complete set of equilibrium equations and the associated boundary conditions are obtained for the plate. Prebuckling loads of the plate are obtained under flatness and axisymmetric deformations. Using the adjacent equilibrium criterion, the linearised stability equations are extracted. An asymmetric stability analysis is performed to obtain the critical buckling loads of the plate and the buckled configurations of the rotating plate. To this end, trigonometric functions through the circumferential direction and the generalised differential quadrature discretization across the radial direction are used which result in an algebraic eigenvalue problem. Benchmark results are given in graphical presentations for combinations of free, simply-supported, sliding supported, and clamped types of boundary conditions. It is shown that rotation enhances the buckling loads of the plate for all types of boundary conditions and alters the buckled shape of the plate.
An attempt is made in the current research to obtain the fundamental buckling torque and the asso... more An attempt is made in the current research to obtain the fundamental buckling torque and the associated buckled shape of an annular plate. The plate is subjected to a torque on its outer edge. An isotropic homogeneous plate is considered. The governing equations of the plate in polar coordinates are established with the aid of the Mindlin plate theory. Deformations and stresses of the plate prior to buckling are determined using the axisymmetric flatness conditions. Small perturbations are then applied to construct the linearised stability equations which govern the onset of buckling. To solve the highly coupled equations in terms of displacements and rotations, periodic auxiliary functions and the generalised differential quadrature method are applied. The coupled linear algebraic equations are a set of homogeneous equations dealing with the buckling state of the plate subjected to a unique torque. Benchmark results are given in tabular presentations for combinations of free, simpl...
The present research considers the free vibration characteristics of a joined shell system that c... more The present research considers the free vibration characteristics of a joined shell system that consists of three segments. The joined shell system contains two conical shells at the ends and a cylindrical shell at the middle. All shell elements are made from isotropic homogeneous material. The shell elements are unified in thickness. With the aid of the first-order shear deformation shell theory and the Donnell type of kinematic assumptions, the equations of motion of a conical shell and the associated boundary conditions are obtained. These equations are valid for each segment. The obtained equations are then discreted using the generalised differential quadratures (GDQ) method. Applying the intersection continuity conditions for displacements, rotations, forces, and moments between two adjacent shells, and also boundary conditions at the ends of the joined shell system, a set of homogeneous equations is obtained, which governs the free vibration motion of the joined shell. Comparisons are made with the available data in the open literature for the case of thin conicalcylindrical-conical shells with special types of geometry or boundary conditions. Afterwards, numerical results are provided for moderately thick shells with different geometrical and boundary conditions.
A R C H I V E O F M E C H A N I C A L E N G I N E E R I N G, 2019
An attempt is made in the current research to obtain the fundamental buckling torque and the asso... more An attempt is made in the current research to obtain the fundamental buckling torque and the associated buckled shape of an annular plate. The plate is subjected to a torque on its outer edge. An isotropic homogeneous plate is considered. The governing equations of the plate in polar coordinates are established with the aid of the Mindlin plate theory. Deformations and stresses of the plate prior to buckling are determined using the axisymmetric flatness conditions. Small perturbations are then applied to construct the linearised stability equations which govern the onset of buckling. To solve the highly coupled equations in terms of displacements and rotations, periodic auxiliary functions and the generalised differential quadrature method are applied. The coupled linear algebraic equations are a set of homogeneous equations dealing with the buckling state of the plate subjected to a unique torque. Benchmark results are given in tabular presentations for combinations of free, simply-supported, and clamped types of boundary conditions. It is shown that the critical buckling torque and its associated shape highly depend upon the combination of boundary conditions, radius ratio, and the thickness ratio.
In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate su... more In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate subjected to uniform compression on both inner and outer edges is analysed. It is further assumed that the plate is rotating with a constant angular speed. Formulation is based on the first order shear deformation plate theory, which is valid for thin and moderately thick plates. The complete set of equilibrium equations and the associated boundary conditions are obtained for the plate. Prebuckling loads of the plate are obtained under flatness and axisymmetric deformations. Using the adjacent equilibrium criterion, the linearised stability equations are extracted. An asymmetric stability analysis is performed to obtain the critical buckling loads of the plate and the buckled configurations of the rotating plate. To this end, trigonometric functions through the circumferential direction and the generalised differential quadrature discretization across the radial direction are used which result in an algebraic eigenvalue problem. Benchmark results are given in graphical presentations for combinations of free, simply-supported, sliding supported, and clamped types of boundary conditions. It is shown that rotation enhances the buckling loads of the plate for all types of boundary conditions and alters the buckled shape of the plate.
Based on the nonlinear dynamic analysis, thermally induced vibrations of the FGM shallow arches s... more Based on the nonlinear dynamic analysis, thermally induced vibrations of the FGM shallow arches subjected to different sudden thermal loads are studied. Temperature and position dependence of the material properties are taken into account. Based on the uncoupled thermoelasticity assumptions, The non-linear one-dimensional transient heat conduction equation is solved numerically by a hybrid iterative GDQ method and Crank-Nicolson time marching scheme. A first order shear deformation arch theory (FSDT) is also combined with the von Kármán type of geometrical non-linearity and the Donnell kinematic assumption to obtain the equations of motion employing the Hamilton principle. Discretization of the highly coupled non-linear equations of motion is done by using the GDQ method in the arch domain. The solution of the system of the ordinary differential equations is established by means of a hybrid iterative Picard-Newmark scheme. Comparison is also made with the existing results for the case of isotropic homogeneous shallow arches, where good agreement is obtained. Also, parametric studies are proposed to show the effects of temperature dependency, geometrical non-linearity, arch thickness, power law index, and the type of thermal-mechanical boundary conditions upon the arch deflection.
Computers & mathematics with applications, Mar 1, 2018
In this investigation, the asymmetrical buckling behaviour of FGM annular plates resting on parti... more In this investigation, the asymmetrical buckling behaviour of FGM annular plates resting on partial Winkler-type elastic foundation under uniform temperature elevation is investigated. Material properties of the plate are assumed to be temperature dependent. Each property of the plate is graded across the thickness direction using a power law function. First order shear deformation plate theory and von Kármán type of geometrical nonlinearity are used to obtain the equilibrium equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained considering the deflection-less conditions. Only plates which are clamped on both inner and outer edges are considered. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The governing equations are divided into two sets. The first set, which is associated with the in-contact region and the second set which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalised differential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved iteratively to obtain the critical conditions of the plate, the associated circumferential mode number and buckled shape of the plate. Benchmark results are given in tabular and graphical presentations dealing with critical buckling temperature and buckled shape of the plate. Numerical results are given to explore the effects of elastic foundation, foundation radius, plate thickness, plate hole size, and power law index of the graded plate. It is shown that, stiffness foundation, and radius of foundation may change the buckled shape of the plate in both circumferential and radial directions. Furthermore, as the stiffness of the foundation or radius of foundation increases, critical buckling temperature of the plate enhances.
Abstract Natural frequencies of a conical–spherical functionally graded material (FGM) shell are ... more Abstract Natural frequencies of a conical–spherical functionally graded material (FGM) shell are obtained in this study. It is assumed that the conical and spherical shell components have identical thickness. The system of joined shell is made from FGMs, where properties of the shell are graded through the thickness direction. The first order shear deformation theory of shells is used to investigate the effects of shear strains and rotary inertia. The Donnel type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations are discretized using the semi-analytical generalized differential quadrature (GDQ) method. Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells with the data of conventional finite element software, parametric studies are carried out for the system of combined moderately thick conical–spherical joined shells made of FGMs and various types of end supports.
The present research deals with the nonaxisymmetric buckling behaviour of isotropic homogeneous a... more The present research deals with the nonaxisymmetric buckling behaviour of isotropic homogeneous annular plates subjected to simultaneous effects of uniform temperature rise and constant angular speed. Firstorder shear deformation plate theory is used to obtain the complete set of governing equations and the associated boundary conditions. Pre-buckling deformations and stresses of the plate are obtained using the solution of a plane stress formulation, neglecting the rotations and lateral deflection. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The resulting equations are solved using a hybrid method, including the exact trigonometric functions through the circumferential direction and generalised differential quadrature method through the radial direction. The resulting eigenvalue problem is solved to obtain the critical conditions of the plate and the associated circumferential mode number. Numerical results reveal that, only for annular plates with exterior edge clamped, rotation may enhance the critical buckling temperature of a plate under special circumstances. Furthermore, asymmetric stability analysis should be performed to extract the critical state and buckled shape of a rotating annular plate subjected to uniform heating. Otherwise, the critical buckling temperature is overestimated and the buckling pattern is wrongly predicted.
Free vibration response of a joined shell system including cylindrical and spherical shells is an... more Free vibration response of a joined shell system including cylindrical and spherical shells is analyzed in this research. It is assumed that the system of joined shell is made from a functionally graded material (FGM). Properties of the shells are assumed to be graded through the thickness. Both shells are unified in thickness. To capture the effects of through-the-thickness shear deformations and rotary inertias, first-order shear deformation theory of shells is used. The Donnell type of kinematic assumptions is adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations is discretized using the semi-analytical generalized differential quadrature method. Considering the clamped and free boundary conditions for the end of the cylindrical shell and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies of the joined shell. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells, some parametric studies are carried out for the system of combined moderately thick cylindrical–spherical shell system. Novel results are provided for the case of FGM joined shells to explore the influence of power-law index and geometric properties.
Free vibration behaviour of a shear deformable conical shell with intermediate ring support is an... more Free vibration behaviour of a shear deformable conical shell with intermediate ring support is analysed in this research. It is assumed that the conical shell is made from a linearly elastic isotropic homogeneous material. To capture the through-thethickness shear deformations and rotary inertia effects, first order shear deformation theory of shells accompanied with the Donnell type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary conditions with the aid of Hamilton's principle. The resulting system of equations are discreted using the semi-analytical generalised differential quadrature (GDQ) method. The shell is divided into two sections, where the continuity conditions are satisfied at the ring position. Considering various types of boundary conditions for the shell ends and continuity conditions at the ring position, an eigenvalue problem is established to examine the natural frequencies of the shell reinforced with an intermediate ring support. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous cylindrical shell with intermediate ring support, parametric studies are carried out for the case of shear deformable conical shells with intermediate ring support.
European Journal of Computational Mechanics, Jan 16, 2019
In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate su... more In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate subjected to uniform compression on both inner and outer edges is analysed. It is further assumed that the plate is rotating with a constant angular speed. Formulation is based on the first order shear deformation plate theory, which is valid for thin and moderately thick plates. The complete set of equilibrium equations and the associated boundary conditions are obtained for the plate. Prebuckling loads of the plate are obtained under flatness and axisymmetric deformations. Using the adjacent equilibrium criterion, the linearised stability equations are extracted. An asymmetric stability analysis is performed to obtain the critical buckling loads of the plate and the buckled configurations of the rotating plate. To this end, trigonometric functions through the circumferential direction and the generalised differential quadrature discretization across the radial direction are used which result in an algebraic eigenvalue problem. Benchmark results are given in graphical presentations for combinations of free, simply-supported, sliding supported, and clamped types of boundary conditions. It is shown that rotation enhances the buckling loads of the plate for all types of boundary conditions and alters the buckled shape of the plate.
In this investigation, the asymmetrical buckling behavior of isotropic homogeneous annular plates... more In this investigation, the asymmetrical buckling behavior of isotropic homogeneous annular plates resting on a partial Winkler-type elastic foundation under uniform temperature elevation is investigated. First-order shear deformation plate theory is used to obtain the governing equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained under the solution of a plane stress formulation, neglecting the rotations and lateral de ection. Applying the adjacent equilibrium criterion, the linearized stability equations are obtained. The governing equations are divided into two sets. The rst set, which is associated with the in-contact region, and the second set, which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalized di erential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved to obtain the critical conditions of the plate and the associated circumferential mode number. Benchmark results are given in tabular and graphical presentations for combinations of simply supported and clamped types of boundary conditions. Numerical results are given to explore the e ects of elastic foundation, foundation radius, plate thickness, plate hole size, and the boundary conditions.
Free vibration analysis of a joined shell system composed of two conical shells is analysed in th... more Free vibration analysis of a joined shell system composed of two conical shells is analysed in this research. It is assumed that the system of joined shell is made from a linearly elastic isotropic homogeneous material. Both shells are unified in thickness. To capture the through-the-thickness shear deformations and rotary inertias, first order theory of shells is accompanied with the Donnell type of kinematic assumptions to establish the general motion equations and the associated boundary and continuity conditions with the aid of Hamilton's principle. The resulted system of equations are discreted using the semi-analytical generalised differential quadrature (GDQ) method. Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies as well as the associated mode shapes. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells, some parametric studies are carried out for the system of combined moderately thick conical-conical.
In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate su... more In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate subjected to uniform compression on both inner and outer edges is analysed. It is further assumed that the plate is rotating with a constant angular speed. Formulation is based on the first order shear deformation plate theory, which is valid for thin and moderately thick plates. The complete set of equilibrium equations and the associated boundary conditions are obtained for the plate. Prebuckling loads of the plate are obtained under flatness and axisymmetric deformations. Using the adjacent equilibrium criterion, the linearised stability equations are extracted. An asymmetric stability analysis is performed to obtain the critical buckling loads of the plate and the buckled configurations of the rotating plate. To this end, trigonometric functions through the circumferential direction and the generalised differential quadrature discretization across the radial direction are used which result in an algebraic eigenvalue problem. Benchmark results are given in graphical presentations for combinations of free, simply-supported, sliding supported, and clamped types of boundary conditions. It is shown that rotation enhances the buckling loads of the plate for all types of boundary conditions and alters the buckled shape of the plate.
An attempt is made in the current research to obtain the fundamental buckling torque and the asso... more An attempt is made in the current research to obtain the fundamental buckling torque and the associated buckled shape of an annular plate. The plate is subjected to a torque on its outer edge. An isotropic homogeneous plate is considered. The governing equations of the plate in polar coordinates are established with the aid of the Mindlin plate theory. Deformations and stresses of the plate prior to buckling are determined using the axisymmetric flatness conditions. Small perturbations are then applied to construct the linearised stability equations which govern the onset of buckling. To solve the highly coupled equations in terms of displacements and rotations, periodic auxiliary functions and the generalised differential quadrature method are applied. The coupled linear algebraic equations are a set of homogeneous equations dealing with the buckling state of the plate subjected to a unique torque. Benchmark results are given in tabular presentations for combinations of free, simpl...
The present research considers the free vibration characteristics of a joined shell system that c... more The present research considers the free vibration characteristics of a joined shell system that consists of three segments. The joined shell system contains two conical shells at the ends and a cylindrical shell at the middle. All shell elements are made from isotropic homogeneous material. The shell elements are unified in thickness. With the aid of the first-order shear deformation shell theory and the Donnell type of kinematic assumptions, the equations of motion of a conical shell and the associated boundary conditions are obtained. These equations are valid for each segment. The obtained equations are then discreted using the generalised differential quadratures (GDQ) method. Applying the intersection continuity conditions for displacements, rotations, forces, and moments between two adjacent shells, and also boundary conditions at the ends of the joined shell system, a set of homogeneous equations is obtained, which governs the free vibration motion of the joined shell. Comparisons are made with the available data in the open literature for the case of thin conicalcylindrical-conical shells with special types of geometry or boundary conditions. Afterwards, numerical results are provided for moderately thick shells with different geometrical and boundary conditions.
A R C H I V E O F M E C H A N I C A L E N G I N E E R I N G, 2019
An attempt is made in the current research to obtain the fundamental buckling torque and the asso... more An attempt is made in the current research to obtain the fundamental buckling torque and the associated buckled shape of an annular plate. The plate is subjected to a torque on its outer edge. An isotropic homogeneous plate is considered. The governing equations of the plate in polar coordinates are established with the aid of the Mindlin plate theory. Deformations and stresses of the plate prior to buckling are determined using the axisymmetric flatness conditions. Small perturbations are then applied to construct the linearised stability equations which govern the onset of buckling. To solve the highly coupled equations in terms of displacements and rotations, periodic auxiliary functions and the generalised differential quadrature method are applied. The coupled linear algebraic equations are a set of homogeneous equations dealing with the buckling state of the plate subjected to a unique torque. Benchmark results are given in tabular presentations for combinations of free, simply-supported, and clamped types of boundary conditions. It is shown that the critical buckling torque and its associated shape highly depend upon the combination of boundary conditions, radius ratio, and the thickness ratio.
In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate su... more In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate subjected to uniform compression on both inner and outer edges is analysed. It is further assumed that the plate is rotating with a constant angular speed. Formulation is based on the first order shear deformation plate theory, which is valid for thin and moderately thick plates. The complete set of equilibrium equations and the associated boundary conditions are obtained for the plate. Prebuckling loads of the plate are obtained under flatness and axisymmetric deformations. Using the adjacent equilibrium criterion, the linearised stability equations are extracted. An asymmetric stability analysis is performed to obtain the critical buckling loads of the plate and the buckled configurations of the rotating plate. To this end, trigonometric functions through the circumferential direction and the generalised differential quadrature discretization across the radial direction are used which result in an algebraic eigenvalue problem. Benchmark results are given in graphical presentations for combinations of free, simply-supported, sliding supported, and clamped types of boundary conditions. It is shown that rotation enhances the buckling loads of the plate for all types of boundary conditions and alters the buckled shape of the plate.
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Papers by Hamed Bagheri