International Journal of Engineering, Science and Technology &b. Lagos, Jul 5, 2011
The effective material properties are predicted for composites with different shape and size of i... more The effective material properties are predicted for composites with different shape and size of inclusions such as cylindrical fibers, spherical and elliptical particles and cylindrical fibers with hemispherical ends. The analysis is based on a numerical homogenization technique using finite element method in connection with three-dimensional representative volume element models. Investigations are carried out to study the influence of various parameters like volume fraction, aspect ratio and particle distribution. Results are discussed and compared.
Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf ... more Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
Finite Elements in Analysis and Design, Nov 1, 2016
The recently proposed Finite Cell Method (FCM) is a combination of higher order Finite Element Me... more The recently proposed Finite Cell Method (FCM) is a combination of higher order Finite Element Methods (FEM) and the Fictitious Domain Concept (FDC). So far, the discretization of the structure under investigation has been based on hexahedral cells when applying the FCM. In the current paper, we extend the FCM to tetrahedral cells offering several advantages over the standard approach. If geometrically complex industrial problems have to be solved, often geometry-conforming tetrahedral meshes already exist. Thus, only micro-structural details that are important for the application, such as pores, need to be resolved by the FDC. Another significant advantage of tetrahedral cells over hexahedral ones is the capability for local mesh refinements. This property is of special interest for problems with sharp gradients and highly localized features where a fine mesh is inevitable. By means of the tetrahedral FCM we can easily analyze the influence of the relevant micro-structural details on the mechanical behavior. The geometry of the micro-structures can be obtained using computed tomography (CT) scans. The data from the CT-scans can then be included into the FCM model in a straightforward fashion. In this paper, the performance and accuracy of the tetrahedral FCM is demonstrated using two examples. The first problem is rather academic and examines a cube with a spherical void. Here, we demonstrate that both the FCM and the FEM achieve the same rates of convergence. As a second example we consider a more practical problem where we investigate the influence of a pore on the stress distribution in an exhaust manifold of a diesel particulate filter (DPF). Again, we observe a very good agreement between the results computed using the FEM and the FCM, respectively.
International Journal of Engineering Science, Apr 1, 2011
This paper deals with unidirectional fiber reinforced composites with rhombic fiber arrangements.... more This paper deals with unidirectional fiber reinforced composites with rhombic fiber arrangements. It is assumed, that there is a periodic structure on micro level, which can be taken by homogenization as a representative volume element (RVE) for the composite, where the composite phases have isotropic or transversely isotropic material characterizations. A special procedure is developed to handle the primary non-rectangular periodicity with common numerical homogenization techniques based on FE-models. Due to appropriate boundary conditions applied to the RVE elastic effective macroscopic coefficients are derived. Results are listed and compared with other publications and good agreements are shown. Furthermore new results are presented, which exhibit the special orthotropic behavior of such composites caused by the rhombic fiber arrangement.
The piezoelectric effect is studied for bending and traction tests for two types of structure con... more The piezoelectric effect is studied for bending and traction tests for two types of structure configurations: homogeneous and composite structures. Mechanical displacements are calculated for traction and bending tests, using FEM for the homogeneous body, where the input material properties are taken from the overall coefficients reported by the Asymptotic Homogenization Method (AHM). A brief theoretical description about the basics of the piezoelectric finite elements and the AHM is given. On the other hand, the calculations of the mechanical displacements are done for the composite structure using FEM where the real data of the material parameters for cylindrical fibers (PZT-5) embedded in a matrix (elastic isotropic polymer) were taken from reported references. A comparison between the results obtained using AHM + FEM and FEM for the homogeneous and the composite structures respectively is reported and shows a favorable result.
Numerical unit cell models of 1-3 periodic composites made of piezoceramic unidirectional cylindr... more Numerical unit cell models of 1-3 periodic composites made of piezoceramic unidirectional cylindrical fibers embedded in a soft non-piezoelectric matrix are developed. The unit cell is used for prediction of the effective coefficients of the periodic transversely isotropic piezoelectric cylindrical fiber composite. Special emphasis is placed on a formulation of the boundary conditions that allows the simulation of all modes of the overall deformation arising from any arbitrary combination of mechanical and electrical loading. The numerical approach is based on the finite element method and it allows extension to composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective properties. For verification, the effective coefficients are evaluated for square and hexagonal arrangements of unidirectional piezoelectric cylindrical fiber composites. The results obtained from the numerical technique are compared with those obtained by means of the analytical asymptotic homogenization method for different volume fractions. Furthermore, the results are compared with other analytical and numerical methods reported in the literature.
The aim of presenting this paper is to evaluate the effective material properties of spherical pa... more The aim of presenting this paper is to evaluate the effective material properties of spherical particle reinforced composites for different volume fractions up to 60%. A numerical homogenization technique based on the finite element method (FEM) with representative volume element (RVE) was used to evaluate the effective material properties with periodic boundary conditions. The numerical approach is based on the FEM and it allows the extension of the composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective material properties. Modified random sequential adsorption algorithm (RSA) was used to generate the three-dimensional RVE models of randomly distributed spherical particles. The effective material properties obtained using the numerical homogenization techniques were compared with different analytical methods and good agreement was achieved. Several investigations had been conducted to estimate the influence of the size of spherical particles and of the RVE on effective material properties of spherical particle reinforced composites.
International Journal of Solids and Structures, Oct 1, 2005
The present work deals with the modeling of 1-3 periodic composites made of piezoceramic (PZT) fi... more The present work deals with the modeling of 1-3 periodic composites made of piezoceramic (PZT) fibers embedded in a soft non-piezoelectric matrix (polymer). We especially focus on predicting the effective coefficients of periodic transversely isotropic piezoelectric fiber composites using representative volume element method (unit cell method). In this paper the focus is on square arrangements of cylindrical fibers in the composite. Two ways for calculating the effective coefficients are presented, an analytical and a numerical approach. The analytical solution is based on the asymptotic homogenization method (AHM) and for the numerical approach the finite element method (FEM) is used. Special attention is given on definition of appropriate boundary conditions for the unit cell to ensure periodicity. With the two introduced methods the effective coefficients were calculated for different fiber volume fractions. Finally the results are compared and discussed.
In this paper unidirectional fiber composites with imperfect interface conditions between the rei... more In this paper unidirectional fiber composites with imperfect interface conditions between the reinforcement and the filler are considered. The microstructure is periodic and the phases have isotropic properties. The periodicity of the microstructure is characterized by a parallelogram. Using the concept of a representative volume element (RVE) a finite element model is developed, in which the distribution of fibers and imperfect contact conditions between interfaces of phases can vary. Applying appropriate periodic boundary conditions to the chosen RVE effective material properties are derived, where those are related to a predefined coordinate system. The homogenization technique is validated by comparing results to literature as far as possible.
Computer Methods in Applied Mechanics and Engineering, Oct 1, 2012
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service... more This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Computer Methods in Applied Mechanics and Engineering 00 (2012) 1-25 Computer methods in applied mechanics and engineering
Proceedings in applied mathematics & mechanics, Dec 1, 2017
Partial differential equations arising in many physical problems are most commonly solved by usin... more Partial differential equations arising in many physical problems are most commonly solved by using the finite element method (FEM). Despite being very versatile, the FEM has one crucial drawback when heterogeneous material systems are considered, i.e. it relies on geometry-conforming discretization. This meshing process often constitutes a bottleneck in the simulation pipeline and therefore needs to be alleviated. One idea is to exploit the benefits of the fictitious domain concept. Here, Cartesian grids can be deployed to straightforwardly discretize an extended domain. In conjunction with higher order shape functions the recently introduced method is referred to as the finite cell method (FCM). The main objective of the contribution at hand is to extend the FCM to arbitrary unstructured meshes. In two-dimensional application polygonal finite elements based on generalized barycentric coordinates are deployed, while the three-dimensional implementation is based on tetrahedral finite elements. A further extension to pyramidal and pentahedral (wedge) elements is, however, straightforward. There are two distinct advantages of using unstructured meshes: (i) a local mesh refinement can easily be conducted and (ii) existing computational models can be re-used for parametric studies. The latter point is important if virtual defects need to be introduced in the ideal model to study their effect on the material behaviour. These possibilities make the unstructured FCM a powerful numerical tool for the investigation of complex highly heterogeneous materials.
ICCES: International Conference on Computational & Experimental Engineering and Sciences, Feb 1, 2009
Abstract Piezoelectric materials have the property of converting electrical energy into mechanica... more Abstract Piezoelectric materials have the property of converting electrical energy into mechanical energy and vice versa. This reciprocity in the energy conversion makes piezoelectric ceramics very attractive for use as sensors and actuators. By combining ...
Proceedings in applied mathematics & mechanics, Dec 1, 2004
The present work deals with the numerical modeling of 1-3 periodic composites made of piezocerami... more The present work deals with the numerical modeling of 1-3 periodic composites made of piezoceramic (PZT) fibers embedded in a soft non-piezoelectric matrix. We especially focus on predicting the effective coefficients of the periodic transversely isotropic piezoelectric fiber composites using representative volume element method (unit cell method). The results which are obtained from the FEM technique are compared with analytical homogenization method for different volume fractions. The effective coefficients are obtained for rectangular and hexagonal arrangement of unidirectional piezoelectric fiber composites.
Proceedings in applied mathematics & mechanics, Dec 1, 2011
A numerical procedure is developed to determine effective material properties of unidirectional f... more A numerical procedure is developed to determine effective material properties of unidirectional fiber reinforced composites with rhombic fiber arrangements. With the assumption of a periodic micro structure a representative volume element (RVE) is considered, where the phases have isotropic or transversely isotropic material characterizations. The interface between the phases is treated as perfect. The procedure handles the primary non-rectangular periodicity with homogenization techniques based on finite element models. Due to appropriate boundary conditions applied to the RVE elastic effective coefficients are derived. Six different boundary condition states are required to get all coefficients of the stiffness tensor. Results are listed and compared with other publications and good agreements are shown. Furthermore new results are presented, which exhibit the orthotropic behavior of such composites caused by the rhombic fiber arrangement.
Proceedings in applied mathematics & mechanics, Dec 1, 2009
The virtual surgery of soft tissues, such as the virtual laparoscopy, requires realistic 3D model... more The virtual surgery of soft tissues, such as the virtual laparoscopy, requires realistic 3D models of all the inner organs belonging to the virtual scenario, which in connection with fast numerical algorithms have to assure the real-time performance of the simulation. The simulation has to take into account the interaction of the surgical instruments with the organs, the contact behavior between the organs including self contact as well as cutting, stitching, bleeding, coagulation etc. Recently, different approaches have been published to achieve a real time performance with sufficient accuracy. In the paper a finite element approach is presented, which includes the geometrical and physical nonlinear dynamic behavior of the organs during the surgery as well as the required contact conditions between the organs and the organs with surgical instruments. Some simplifications of the standard procedure (contact search, updating rate, etc.) to increase the computational speed as well as the beneficial behavior of an implicit time integration scheme resulting in larger time steps are discussed. In the paper some examples are presented to demonstrate the performance and the accuracy of the approach.
In recent years a steadily growing interest in online monitoring or structural health monitoring ... more In recent years a steadily growing interest in online monitoring or structural health monitoring (SHM) of lightweight structures is seen, as SHM systems hold the promise to increase the safety and more importantly reduce maintenance costs of structures. A promising approach, in thin-walled structures, to reach the aforementioned goals is a Lamb wave based damage detection device. Currently guided waves are excited utilizing surface-bonded piezoelectric transducers. To be able to predict the wave propagation as well as the behaviour of the piezoelectric actuator/sensor accurately higher order Finite-Element-Methods (p-FEM) are am important numerical tool. Dealing with ultrasonic waves in thin-walled structures conventional linear or quadratic finite elements quickly reach their limit and are not suitable to obtain good quality results at manageable numerical costs. Additionally, even complex electrode geometries can be modelled easily using a p-FEM scheme. Thus, it is the objective of this contribution to develop different types of higher order hexahedral finite elements. They are either based on the normalized integrals of the Legendre polynomials or on non-uniform rational B-spline (NURBS). The capability of this approach is then demonstrated by computing the Lamb wave propagation in a stringer stiffened carbon fibre reinforced plastic (CFRP) plate.
International Journal of Engineering, Science and Technology &b. Lagos, Jul 5, 2011
The effective material properties are predicted for composites with different shape and size of i... more The effective material properties are predicted for composites with different shape and size of inclusions such as cylindrical fibers, spherical and elliptical particles and cylindrical fibers with hemispherical ends. The analysis is based on a numerical homogenization technique using finite element method in connection with three-dimensional representative volume element models. Investigations are carried out to study the influence of various parameters like volume fraction, aspect ratio and particle distribution. Results are discussed and compared.
Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf ... more Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
Finite Elements in Analysis and Design, Nov 1, 2016
The recently proposed Finite Cell Method (FCM) is a combination of higher order Finite Element Me... more The recently proposed Finite Cell Method (FCM) is a combination of higher order Finite Element Methods (FEM) and the Fictitious Domain Concept (FDC). So far, the discretization of the structure under investigation has been based on hexahedral cells when applying the FCM. In the current paper, we extend the FCM to tetrahedral cells offering several advantages over the standard approach. If geometrically complex industrial problems have to be solved, often geometry-conforming tetrahedral meshes already exist. Thus, only micro-structural details that are important for the application, such as pores, need to be resolved by the FDC. Another significant advantage of tetrahedral cells over hexahedral ones is the capability for local mesh refinements. This property is of special interest for problems with sharp gradients and highly localized features where a fine mesh is inevitable. By means of the tetrahedral FCM we can easily analyze the influence of the relevant micro-structural details on the mechanical behavior. The geometry of the micro-structures can be obtained using computed tomography (CT) scans. The data from the CT-scans can then be included into the FCM model in a straightforward fashion. In this paper, the performance and accuracy of the tetrahedral FCM is demonstrated using two examples. The first problem is rather academic and examines a cube with a spherical void. Here, we demonstrate that both the FCM and the FEM achieve the same rates of convergence. As a second example we consider a more practical problem where we investigate the influence of a pore on the stress distribution in an exhaust manifold of a diesel particulate filter (DPF). Again, we observe a very good agreement between the results computed using the FEM and the FCM, respectively.
International Journal of Engineering Science, Apr 1, 2011
This paper deals with unidirectional fiber reinforced composites with rhombic fiber arrangements.... more This paper deals with unidirectional fiber reinforced composites with rhombic fiber arrangements. It is assumed, that there is a periodic structure on micro level, which can be taken by homogenization as a representative volume element (RVE) for the composite, where the composite phases have isotropic or transversely isotropic material characterizations. A special procedure is developed to handle the primary non-rectangular periodicity with common numerical homogenization techniques based on FE-models. Due to appropriate boundary conditions applied to the RVE elastic effective macroscopic coefficients are derived. Results are listed and compared with other publications and good agreements are shown. Furthermore new results are presented, which exhibit the special orthotropic behavior of such composites caused by the rhombic fiber arrangement.
The piezoelectric effect is studied for bending and traction tests for two types of structure con... more The piezoelectric effect is studied for bending and traction tests for two types of structure configurations: homogeneous and composite structures. Mechanical displacements are calculated for traction and bending tests, using FEM for the homogeneous body, where the input material properties are taken from the overall coefficients reported by the Asymptotic Homogenization Method (AHM). A brief theoretical description about the basics of the piezoelectric finite elements and the AHM is given. On the other hand, the calculations of the mechanical displacements are done for the composite structure using FEM where the real data of the material parameters for cylindrical fibers (PZT-5) embedded in a matrix (elastic isotropic polymer) were taken from reported references. A comparison between the results obtained using AHM + FEM and FEM for the homogeneous and the composite structures respectively is reported and shows a favorable result.
Numerical unit cell models of 1-3 periodic composites made of piezoceramic unidirectional cylindr... more Numerical unit cell models of 1-3 periodic composites made of piezoceramic unidirectional cylindrical fibers embedded in a soft non-piezoelectric matrix are developed. The unit cell is used for prediction of the effective coefficients of the periodic transversely isotropic piezoelectric cylindrical fiber composite. Special emphasis is placed on a formulation of the boundary conditions that allows the simulation of all modes of the overall deformation arising from any arbitrary combination of mechanical and electrical loading. The numerical approach is based on the finite element method and it allows extension to composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective properties. For verification, the effective coefficients are evaluated for square and hexagonal arrangements of unidirectional piezoelectric cylindrical fiber composites. The results obtained from the numerical technique are compared with those obtained by means of the analytical asymptotic homogenization method for different volume fractions. Furthermore, the results are compared with other analytical and numerical methods reported in the literature.
The aim of presenting this paper is to evaluate the effective material properties of spherical pa... more The aim of presenting this paper is to evaluate the effective material properties of spherical particle reinforced composites for different volume fractions up to 60%. A numerical homogenization technique based on the finite element method (FEM) with representative volume element (RVE) was used to evaluate the effective material properties with periodic boundary conditions. The numerical approach is based on the FEM and it allows the extension of the composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective material properties. Modified random sequential adsorption algorithm (RSA) was used to generate the three-dimensional RVE models of randomly distributed spherical particles. The effective material properties obtained using the numerical homogenization techniques were compared with different analytical methods and good agreement was achieved. Several investigations had been conducted to estimate the influence of the size of spherical particles and of the RVE on effective material properties of spherical particle reinforced composites.
International Journal of Solids and Structures, Oct 1, 2005
The present work deals with the modeling of 1-3 periodic composites made of piezoceramic (PZT) fi... more The present work deals with the modeling of 1-3 periodic composites made of piezoceramic (PZT) fibers embedded in a soft non-piezoelectric matrix (polymer). We especially focus on predicting the effective coefficients of periodic transversely isotropic piezoelectric fiber composites using representative volume element method (unit cell method). In this paper the focus is on square arrangements of cylindrical fibers in the composite. Two ways for calculating the effective coefficients are presented, an analytical and a numerical approach. The analytical solution is based on the asymptotic homogenization method (AHM) and for the numerical approach the finite element method (FEM) is used. Special attention is given on definition of appropriate boundary conditions for the unit cell to ensure periodicity. With the two introduced methods the effective coefficients were calculated for different fiber volume fractions. Finally the results are compared and discussed.
In this paper unidirectional fiber composites with imperfect interface conditions between the rei... more In this paper unidirectional fiber composites with imperfect interface conditions between the reinforcement and the filler are considered. The microstructure is periodic and the phases have isotropic properties. The periodicity of the microstructure is characterized by a parallelogram. Using the concept of a representative volume element (RVE) a finite element model is developed, in which the distribution of fibers and imperfect contact conditions between interfaces of phases can vary. Applying appropriate periodic boundary conditions to the chosen RVE effective material properties are derived, where those are related to a predefined coordinate system. The homogenization technique is validated by comparing results to literature as far as possible.
Computer Methods in Applied Mechanics and Engineering, Oct 1, 2012
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service... more This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Computer Methods in Applied Mechanics and Engineering 00 (2012) 1-25 Computer methods in applied mechanics and engineering
Proceedings in applied mathematics & mechanics, Dec 1, 2017
Partial differential equations arising in many physical problems are most commonly solved by usin... more Partial differential equations arising in many physical problems are most commonly solved by using the finite element method (FEM). Despite being very versatile, the FEM has one crucial drawback when heterogeneous material systems are considered, i.e. it relies on geometry-conforming discretization. This meshing process often constitutes a bottleneck in the simulation pipeline and therefore needs to be alleviated. One idea is to exploit the benefits of the fictitious domain concept. Here, Cartesian grids can be deployed to straightforwardly discretize an extended domain. In conjunction with higher order shape functions the recently introduced method is referred to as the finite cell method (FCM). The main objective of the contribution at hand is to extend the FCM to arbitrary unstructured meshes. In two-dimensional application polygonal finite elements based on generalized barycentric coordinates are deployed, while the three-dimensional implementation is based on tetrahedral finite elements. A further extension to pyramidal and pentahedral (wedge) elements is, however, straightforward. There are two distinct advantages of using unstructured meshes: (i) a local mesh refinement can easily be conducted and (ii) existing computational models can be re-used for parametric studies. The latter point is important if virtual defects need to be introduced in the ideal model to study their effect on the material behaviour. These possibilities make the unstructured FCM a powerful numerical tool for the investigation of complex highly heterogeneous materials.
ICCES: International Conference on Computational & Experimental Engineering and Sciences, Feb 1, 2009
Abstract Piezoelectric materials have the property of converting electrical energy into mechanica... more Abstract Piezoelectric materials have the property of converting electrical energy into mechanical energy and vice versa. This reciprocity in the energy conversion makes piezoelectric ceramics very attractive for use as sensors and actuators. By combining ...
Proceedings in applied mathematics & mechanics, Dec 1, 2004
The present work deals with the numerical modeling of 1-3 periodic composites made of piezocerami... more The present work deals with the numerical modeling of 1-3 periodic composites made of piezoceramic (PZT) fibers embedded in a soft non-piezoelectric matrix. We especially focus on predicting the effective coefficients of the periodic transversely isotropic piezoelectric fiber composites using representative volume element method (unit cell method). The results which are obtained from the FEM technique are compared with analytical homogenization method for different volume fractions. The effective coefficients are obtained for rectangular and hexagonal arrangement of unidirectional piezoelectric fiber composites.
Proceedings in applied mathematics & mechanics, Dec 1, 2011
A numerical procedure is developed to determine effective material properties of unidirectional f... more A numerical procedure is developed to determine effective material properties of unidirectional fiber reinforced composites with rhombic fiber arrangements. With the assumption of a periodic micro structure a representative volume element (RVE) is considered, where the phases have isotropic or transversely isotropic material characterizations. The interface between the phases is treated as perfect. The procedure handles the primary non-rectangular periodicity with homogenization techniques based on finite element models. Due to appropriate boundary conditions applied to the RVE elastic effective coefficients are derived. Six different boundary condition states are required to get all coefficients of the stiffness tensor. Results are listed and compared with other publications and good agreements are shown. Furthermore new results are presented, which exhibit the orthotropic behavior of such composites caused by the rhombic fiber arrangement.
Proceedings in applied mathematics & mechanics, Dec 1, 2009
The virtual surgery of soft tissues, such as the virtual laparoscopy, requires realistic 3D model... more The virtual surgery of soft tissues, such as the virtual laparoscopy, requires realistic 3D models of all the inner organs belonging to the virtual scenario, which in connection with fast numerical algorithms have to assure the real-time performance of the simulation. The simulation has to take into account the interaction of the surgical instruments with the organs, the contact behavior between the organs including self contact as well as cutting, stitching, bleeding, coagulation etc. Recently, different approaches have been published to achieve a real time performance with sufficient accuracy. In the paper a finite element approach is presented, which includes the geometrical and physical nonlinear dynamic behavior of the organs during the surgery as well as the required contact conditions between the organs and the organs with surgical instruments. Some simplifications of the standard procedure (contact search, updating rate, etc.) to increase the computational speed as well as the beneficial behavior of an implicit time integration scheme resulting in larger time steps are discussed. In the paper some examples are presented to demonstrate the performance and the accuracy of the approach.
In recent years a steadily growing interest in online monitoring or structural health monitoring ... more In recent years a steadily growing interest in online monitoring or structural health monitoring (SHM) of lightweight structures is seen, as SHM systems hold the promise to increase the safety and more importantly reduce maintenance costs of structures. A promising approach, in thin-walled structures, to reach the aforementioned goals is a Lamb wave based damage detection device. Currently guided waves are excited utilizing surface-bonded piezoelectric transducers. To be able to predict the wave propagation as well as the behaviour of the piezoelectric actuator/sensor accurately higher order Finite-Element-Methods (p-FEM) are am important numerical tool. Dealing with ultrasonic waves in thin-walled structures conventional linear or quadratic finite elements quickly reach their limit and are not suitable to obtain good quality results at manageable numerical costs. Additionally, even complex electrode geometries can be modelled easily using a p-FEM scheme. Thus, it is the objective of this contribution to develop different types of higher order hexahedral finite elements. They are either based on the normalized integrals of the Legendre polynomials or on non-uniform rational B-spline (NURBS). The capability of this approach is then demonstrated by computing the Lamb wave propagation in a stringer stiffened carbon fibre reinforced plastic (CFRP) plate.
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