Showing papers in "Engineering Computations in 1993"
TL;DR: In this article, three different approaches are scrutinized which may be used to remedy these two intimately related deficiencies of the classical theory, namely (i) the addition of higher-order deformation gradients, (ii) the use of micropolar continuum models, and (iii) the adding of rate dependence.
Abstract: Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from excessive mesh dependence when strain‐softening models are used in numerical analyses and cannot reproduce the size effect commonly observed in quasi‐brittle failure. In this contribution three different approaches will be scrutinized which may be used to remedy these two intimately related deficiencies of the classical theory, namely (i) the addition of higher‐order deformation gradients, (ii) the use of micropolar continuum models, and (iii) the addition of rate dependence. By means of a number of numerical simulations it will be investigated under which conditions these enriched continuum theories permit localization of deformation without losing ellipticity for static problems and hyperbolicity for dynamic problems. For the latter class of problems the crucial role of dispersion in wave propagation in strain‐softening media will also be highlighted.
598 citations
TL;DR: In this article, a finite element model for numerical simulation of non-steady but continuous chip formation under orthogonal cutting conditions is described, where the problem is treated as coupled thermo-mechanical.
Abstract: A finite element model for numerical simulation of non‐steady but continuous chip formation under orthogonal cutting conditions is described. The problem is treated as coupled thermo‐mechanical. A velocity approach has been adopted for the proposed solution. The computational algorithm takes care of dynamic contact conditions and makes use of an automatic remeshing procedure. The results of simulation yield complete history of chip initiation and growth as well as distributions of strain rate, strain, stress and temperature. The paper includes a detailed presentation of computational results for an illustrative case.
117 citations
TL;DR: In this paper, a general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented, which is based on the combination of a standard C0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of a deflection gradient along the sides using a finite volume-like approach.
Abstract: A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of the deflection gradient along the sides using a finite volume‐like approach. The formulation is particularized for the simplest element of the family, i.e. the three node triangle with three degrees of freedom. The potential of the new element is shown through different examples of application.
88 citations
TL;DR: The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited and it is shown that the correct evaluation of the convergence rate of the error norms involved in the error measure and the optimal mesh criteria chosen are essential to avoid oscillations in the refinement process.
Abstract: The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error norms involved in the error measure and the optimal mesh criteria chosen are essential to avoid oscillations in the refinement process. Two mesh optimality criteria based on: (a) the equal distribution of global error, and (b) the specific error over the elements are studied and compared in detail through some examples of application.
74 citations
TL;DR: In this article, the wavelet technique is used to solve Poisson's equation in two dimensions and Dirichlet boundary conditions are imposed using the capacitance matrix method described by Proskurowski and Widlund and others.
Abstract: We describe how wavelets may be used to solve partial differential equations. These problems are currently solved by techniques such as finite differences, finite elements and multigrid. The wavelet method, however, offers several advantages over traditional methods. Wavelets have the ability to represent functions at different levels of resolution, thereby providing a logical means of developing a hierarchy of solutions. Furthermore, compactly supported wavelets (such as those due to Daubechies) are localized in space, which means that the solution can be refined in regions of high gradient, e.g. stress concentrations, without having to regenerate the mesh for the entire problem. To demonstrate the wavelet technique, we consider Poisson's equation in two dimensions. By comparison with a simple finite difference solution to this problem with periodic boundary conditions we show how a wavelet technique may be efficiently developed. Dirichlet boundary conditions are then imposed, using the capacitance matrix method described by Proskurowski and Widlund and others. The convergence of the wavelet solutions are examined and they are found to compare extremely favourably to the finite difference solutions. Preliminary investigations also indicate that the wavelet technique is a strong contender to the finite element method.
54 citations
TL;DR: An object oriented finite element model is presented, in which the finite elements are represented in the form of a hierarchical tree by which it is possible to develop elements by programming only the differences from existing elements.
Abstract: An object oriented finite element model is presented. The main advantage of this model over conventional systems is that, the additional code required for adding elements to the finite element library is minimal. The powerful mechanisms provided by object oriented systems facilitate this. These mechanisms enable re‐use of existing code, and allow the programmer to leave certain operations to the computer, which, without object oriented techniques, would not have been possible. In the above model, the finite elements are represented in the form of a hierarchical tree by which it is possible to develop elements by programming only the differences from existing elements. Suitable object oriented designs have been developed for representing mathematical entities like differential operators and shape functions, with a view to automating the process of development of element properties, so that, the element developer needs to specify just the minimum details, leaving most of the operations to the computer. Some of the concepts in object oriented programming are explained in detail, with the examples used in the above model.
29 citations
TL;DR: In this article, the pseudo-concentrations technique and a quadrilateral element based on mixed interpolation of tensorial components (QMITC) were used for modeling 2D metal forming processes.
Abstract: In order to develop an engineering tool for modelling 2D metal forming processes we implemented in the flow formulation the pseudo‐concentrations technique and a quadrilateral element based on mixed interpolation of tensorial components (QMITC). By doing this we obtained a reliable and efficient Eulerian formulation for modelling steady and transient metal forming problems. Some cases were analysed in order to test the performance of the formulation.
27 citations
TL;DR: In this paper, the problem of designing reinforced concrete plates and shells has interested researchers for a long time and the recent development of the computers' performance and storage capacity combined with powerful numerical methods revealed the need of a clear procedure to design elements subjected to membrane and flexure forces.
Abstract: The problem of designing reinforced concrete plates and shells has interested researchers for a long time. The recent development of the computers' performance and storage capacity combined with powerful numerical methods revealed the need of a clear procedure to design elements subjected to membrane and flexure forces. In the present study this problem is formulated based on the equilibrium conditions and an iterative procedure is suggested. The computational code based on this approach is given, as well as some examples of the method.
23 citations
TL;DR: An efficient implementation of a constitutive model for reinforced concrete plates is discussed in this article, which is set directly in terms of stress resultants and their energy conjugate strain measures, relating their total values.
Abstract: An efficient implementation of a constitutive model for reinforced concrete plates is discussed in this work. The constitutive model is set directly in terms of stress resultants and their energy conjugate strain measures, relating their total values. The latter simplification is justified by our primary goal being an evaluation of the limit load of a reinforced concrete plate. A concept of the ‘rotating crack model’ is utilized in proposing the constitutive model to relate the principal values of bending moments and the corresponding values of curvatures. Efficient implementation is provided by a very robust, but inexpensive plate element. The element is based on an assumed shear strain field and a set of incompatible bending modes, which provides that the non‐linear computations, pertinent to constitutive model, can be carried out locally, i.e. independently at each numerical integration point. Set of numerical examples is presented to demonstrate a very satisfying performance of the proposed model.
22 citations
TL;DR: In this paper, the transverse stresses that are generated within the interface between two layers of laminated composite and sandwich laminates were evaluated by using Cℴ finite element formulation of higher-order theories.
Abstract: This paper attempts to evaluate the transverse stresses that are generated within the interface between two layers of laminated composite and sandwich laminates by using Cℴ finite element formulation of higher‐order theories. These theories do not require the use of a fictitious shear correction coefficient which is usually associated with the first‐order Reissner‐Mindlin theory. The in‐plane stresses are evaluated by using constitutive relations. The transverse stresses are evaluated through the use of equilibrium equations. The integration of the equilibrium equations is attempted through forward and central direct finite difference techniques and a new approach, named as, an exact surface fitting method. Sixteen and nine‐noded quadrilateral Lagrangian elements are used. The numerical results obtained by the present approaches in general and the exact surface fitting method in particular, show excellent agreement with available elasticity solutions. New results for symmetric sandwich laminates are also presented for future comparisons.
18 citations
TL;DR: A new algorithm for reducing the profile and root‐mean‐square wavefront of sparse matrices with a symmetric structure is presented, which is fast, simple and useful in engineering analysis where it can be employed to derive efficient orderings for both profile and frontal solution schemes.
Abstract: A new algorithm for reducing the profile and root‐mean‐square wavefront of sparse matrices with a symmetric structure is presented. Our numerical experiments show an overall better performance than the widely used reverse Cuthill‐McKee, Gibbs‐King and Sloan algorithms. The new algorithm is fast, simple and useful in engineering analysis where it can be employed to derive efficient orderings for both profile and frontal solution schemes.
TL;DR: In this article, a simplified method to simulate damage evolution in heterogeneous media from geodesic propagation calculations is proposed, which is based on a minimization of the fracture energy criterion, ignoring the local variations of the stored strain energy.
Abstract: We propose a simplified method to simulate damage evolution in heterogeneous media from geodesic propagation calculations. The method introduced for the case of porous media (polycrystalline graphite), was generalized to multiphase media, and then to a continuous variation of local fracture energy. It is based on a minimization of the fracture energy criterion, ignoring the local variations of the stored strain energy. With this simplification, the microcracking process is simulated by very efficient algorithms, involving a low calculation cost, to extract minimal paths on graphs with edges valued according to the local fracture energy. From the simulations, made on micrographs in materials or on random microstructure simulations, we get images of the possible microcracks paths, to be compared with real cracking of materials, and an estimation of the effective toughness of heterogeneous materials. Our approach is illustrated from two‐dimensional simulations corresponding to various types of microstructure involving the following micro‐geometrical distributions of the local fracture energy: isotropic and anisotropic two‐phase media, polycrystal with cleavage and intergranular fracture, material with a continuous distribution of surface energy.
TL;DR: In this article, the mixed assumed strain approach proposed by Simo and Rifai is used to derive three 8-noded hexahedral mixed strain elements for geometrically nonlinear problems.
Abstract: The mixed assumed strain approach proposed by Simo and Rifai is used to derive three 8‐noded hexahedral mixed strain elements. The approach is also generalized to geometrically non‐linear problems. Based on the Galerkin form of Hu‐Washizu three field variational principle, the Green‐Lagrange strain tensor and the second Piola‐Kirchhoff stress tensor (symmetric) are employed to develop the geometrically non‐linear formulation for 2D and 3D mixed enhanced strain elements. Numerical results are presented to show that the resulting hexahedral mixed strain elements possess all the ideal qualities. They are able to pass the patch test, do not exhibit the false shear phenomena and do not lock for nearly incompressible materials. Also, they are less sensitive to distorted meshes than standard isoparametric elements and exhibit high accuracy for both linear and non‐linear problems, permitting coarse discretizations to be utilized. The elements developed in this paper have been implemented in the general purpose FE package LUSAS.
TL;DR: In this paper, a finite element model for large strain elastoplastic problems was developed for the analysis of void volume fraction and hydrostatic stress, and three types of computations were proposed: axisymmetric Q4 element traction are given as validation example; second, collar cylinder compression are computed as reference example; third, bulk forming are analysed as large strain specific example.
Abstract: Microstructure void volume fraction is taken into account in finite element models developed for large strain elastoplastic problems. Void nucleation rate is related to matrix effective strain rate, void growth to material strain rate and associated elastoplastic potential available for porous material, void coalescence to matrix effective strain rate. The related radial return algorithm is described. Three types of computations are proposed: first, axisymmetric Q4 element traction are given as validation example; second, collar cylinder compression are computed as reference example; third, bulk forming are analysed as large strain specific example. Void volume fraction and hydrostatic stress are mainly discussed according to microvoids nucleation, growth and coalescence. Finally, the main interests of those computations are enhanced.
TL;DR: In this paper, the stiffness degrading model based on the total stress-strain constitutive relationship and the tangent softening model are implemented using a new softening initiation criterion proposed for application in multi-dimensional finite element analysis.
Abstract: The localized strain softening behaviour of concrete has been modelled by two approaches: (i) the stiffness degrading model based on the total stress‐strain constitutive relationship, and (ii) the tangent softening model based on the incremental stress‐strain relationship. The models are implemented using a new softening initiation criterion proposed for application in multi‐dimensional finite element analysis. Parametric analyses on plain concrete beams, tested experimentally by other researchers, have been carried out to investigate the required numerical efforts, the mesh objectivity, and the energy dissipation characteristics of the structures. The stiffness degrading model is very stable even when applied with relatively coarse finite element meshes. However, the computational demand of this model is relatively high. The combination of a total stress‐strain constitutive relationship to compute the element responses, and an incremental relationship to formulate the stiffness matrix, appears to be computationally efficient and stable, provided that adequately refined finite element mesh is used to model the structure.
TL;DR: A new approach for estimating the discretization error of finite element analysis of generalized eigenproblems using smoothed gradients at nodal points to derive improved element‐by‐element interpolation functions and their gradients are used in the Rayleigh quotient to obtain an improved eigenvalue.
Abstract: This paper presents a new approach for estimating the discretization error of finite element analysis of generalized eigenproblems. The method uses smoothed gradients at nodal points to derive improved element‐by‐element interpolation functions. The improved interpolation functions and their gradients are used in the Rayleigh quotient to obtain an improved eigenvalue. The improved eigenvalue is used to estimate the error of the original solution. The proposed method does not require any re‐solution of the eigenproblem. Results for 1‐D and 2‐D C° eigenproblems in acoustics and elastic vibrations are used as examples to demonstrate the accuracy of the proposed method.
TL;DR: In this article, the authors compare the convergence of the elastic slip law for increasing stiffness and the convergence behavior of the adopted Newton iterations for a given law for a class of nonlinear slip criteria.
Abstract: Finite element implementations of the classical (stick‐slip) and a regularized (elastic‐slip) friction laws are compared for a class of non‐linear slip criteria. The fully implicit method is used for integrating the friction law. A novel implementation of the stick‐slip law, that involved transformation to a non‐orthogonal coordinate system at each contact point, is assessed. A numerical comparison is carried out for a simple problem, that has previously been analysed in the literature. The convergence of the elastic‐slip law for increasing stiffness is evaluated in addition to convergence behaviour of the adopted Newton iterations for a given law.
TL;DR: In this paper, a finite strip method is used to determine the natural frequencies and modal shapes based on Mindlin-Reissner shell theory which allows for transverse shear deformation and rotatory inertia effects.
Abstract: This paper deals with structural shape optimization of vibrating prismatic shells and folded plates. The finite strip method is used to determine the natural frequencies and modal shapes based on Mindlin‐Reissner shell theory which allows for transverse shear deformation and rotatory inertia effects. An automated optimization procedure is adopted which integrates finite strip analysis, parametric cubic spline geometry definition, automatic mesh generation, sensitivity analysis and mathematical programming methods. The objective is to maximize the fundamental frequency by changing thickness and shape design variables defining the cross‐section of the structure, with a constraint that the total volume of the structure remains constant. A series of examples is presented to highlight various features of the optimization procedure as well as the accuracy and efficiency of finite strip method.
TL;DR: In this article, the response of reinforced concrete slabs subjected to central patch loads using nonlinear finite element analysis was analyzed. But the sensitivity of various components of material model was not considered.
Abstract: This paper presents the full range sensitivity study of various components of material model on the response of reinforced concrete slabs subjected to central patch loads using non‐linear finite element analysis. A layered degenerate quadratic plate element with five degrees of freedom was employed. Smeared crack model was used with orthogonal cracking. The components considered in this work are: perfectly plastic models versus hardening models, role of crushing condition on collapse load, influence of dowel effect on punching capacity, parametric variation of tension stiffening parameter, parametric variation of degraded shear modulus and the role of yield criterion.
TL;DR: In this paper, the authors demonstrate the application of a GA to a simple inverse thermal field problem, and compare its performance against a relatively mature technique for the solution of such problems, and indicate that, despite the relatively large computational cost of GAs, their accuracy and robustness warrants further investigation of their performance in more demanding applications.
Abstract: In principle, it is possible to apply genetic algorithms (GAs) to the solution of inverse problems in the simulation of manufacturing processes. In this context, an inverse problem can be stated as ‘knowing the desired output of a process, what combination of process parameters are required for its achievement?’. Since the simulation of many processes requires the simulation of thermal, solids and/or fluids problems, the application of GAs to inverse process modelling depends on their ability to solve a wide range of inverse field problems. This paper has two major objectives: (a) to demonstrate the application of a GA to a simple inverse thermal field problem, and (b) to compare its performance against a relatively mature technique for the solution of such problems. The results of this study indicate that, despite the relatively large computational cost of GAs, their accuracy and robustness warrants further investigation of their performance in more demanding applications.
TL;DR: In this paper, an enhanced procedure which circumvents the limitations of the interface variables model and hierarchical model is proposed, where each material layer of the beam element is covered by one quadrilateral 9-node element, providing a parabolic approximation of displacements.
Abstract: The stress recovery procedures discussed in the present paper refer to a multi‐layered element of assembled Timoshenko beam elements. Directly calculated stresses for a multi‐layered beam model strongly depend on properties of the approximation functions, and are unrealistic. Thus, an enhanced procedure which circumvents the limitations of the interface variables model, and hierarchical model is proposed. Each material layer of the beam element is covered by one quadrilateral 9‐node element, providing a parabolic approximation of displacements. The stresses are evaluated using 2 × 2 Gauss points, projected to corner nodes, and smoothed within material layers. Numerical calculations show very good accordance of stresses yielded by this procedure with 2D results.
TL;DR: A sheet metal forming simulation code has been developed, based on the explicit time integration scheme and Mindlin shell theory, which has been used for the analysis of a number of industrial parts as discussed by the authors.
Abstract: A sheet metal forming simulation code has been developed, based on the explicit time integration scheme and Mindlin shell theory. It has been used for the analysis of a number of industrial parts. After recalling some modelling issues, this paper describes an industrial methodology based on the experience of those analyses. The aim of the methodology is to provide, at early design stage, information on the product formability with a workload and lead time adapted to the design delays. Concurrently 2D analyses, critical zones studies and coarse mesh global investigations can be used, with a flexible number of iterations, prior to full refined analyses of the forming process. The application of the methodology on several industrial examples is discussed.
TL;DR: A fully parallel algorithm for the solution of a finite element system using a MIMD (multiple‐instruction multiple‐data architecture) parallel computer is presented and the inherently sequential Gauss‐Seidel and SOR schemes are altered into fully parallel iterative schemes.
Abstract: A fully parallel algorithm for the solution of a finite element system using a MIMD (multiple‐instruction multiple‐data architecture) parallel computer is presented The formulation includes a simple domain decomposer that automatically divides a finite element mesh into a list of subdomains to guarantee the load balancing Furthermore, each subdomain is assigned to a processor of a parallel computer and treated as a sub‐finite element system with information exchanged through the interface between two adjacent subdomains With this new algorithm, these sub‐finite element systems are solved fully parallelly as independent finite element systems, not only the computations of the interior nodes but also the computations of the interface nodes can be executed parallelly Also, the inherently sequential Gauss‐Seidel and SOR schemes are altered into fully parallel iterative schemes An implementation of this new scheme on an iPSC/2 D5 Hypercube Concurrent Computer reached an efficiency of more than 100% when c
TL;DR: Two non‐linear finite element programs have been restructured by using vectorization techniques in order to run efficiently on the Cray X‐MP/416 to take advantage of the four processors of the machine.
Abstract: Two non‐linear finite element programs have been restructured by using vectorization techniques in order to run efficiently on the Cray X‐MP/416. One of them has also been multi‐tasked to take advantage of the four processors of the machine. The techniques used in restructuring the software are discussed, and it is shown that each program must be treated individually. The resulting speed enhancements are shown to be program dependent, with a speed‐up of approximately 20 being achieved with one of the programs.
TL;DR: In this paper, the buckling analysis of prismatic folded plate structures supported on diaphragms at two opposite edges is carried out using variable thickness finite strips based on Mindlin-Reissner assumptions which allow for transverse shear deformation effects.
Abstract: This paper deals with the buckling analysis of prismatic folded plate structures supported on diaphragms at two opposite edges. The analysis is carried out using variable thickness finite strips based on Mindlin‐Reissner assumptions which allow for transverse shear deformation effects. The theoretical formulation is presented for a family of C(0) strips and the accuracy and relative performance of the strips are examined. Results are presented for a series of problems including plates and stiffened panels. In a companion paper these accurate and inexpensive finite strips are used in the context of structural shape optimization.
TL;DR: In this paper, the optimal thickness distribution of variable thickness plates and shells is investigated by using a structural optimization algorithm which integrates the Coons patch technique for thickness definition, structural analysis using 9-node Huang-Hinton shell elements, sensitivity evaluation using the global finite difference method and the sequential quadratic programming method.
Abstract: The optimization of variable thickness plates and shells is studied. In particular, three types of shell are considered: hyperbolic paraboloid, conoid and cylindrical shell. The main objective is to investigate the optimal thickness distributions as the geometric form of the structure changes from a plate to a deep shell. The optimal thickness distribution is found by use of a structural optimization algorithm which integrates the Coons patch technique for thickness definition, structural analysis using 9‐node Huang‐Hinton shell elements, sensitivity evaluation using the global finite difference method and the sequential quadratic programming method. The composition of the strain energy is monitored during the optimization process to obtain insight into the energy distribution for the optimum structures. Several benchmark examples are considered illustrating optimal thickness variations under different loading, boundary and design variable linking conditions.
TL;DR: In this paper, rank analysis of a rectangular matrix of a homogeneous set of incremental equations regarded as an element of continuation method is presented, based on a known feature that every rectangular matrix can be transformed into the matrix of echelon form.
Abstract: This paper is concerned with rank analysis of rectangular matrix of a homogeneous set of incremental equations regarded as an element of continuation method. The rank analysis is based on a known feature that every rectangular matrix can be transformed into the matrix of echelon form. By inspection of the rank, correct control parameters are chosen and this allows not only for rounding limit and turning points but also for branch‐switching near bifurcation points.
TL;DR: In this article, a unified approach for the pseudo-transient (static) linear and geometrically nonlinear analyses of composite laminates is presented, where an explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices.
Abstract: A unified approach is presented for the pseudo‐transient (static) linear and geometrically non‐linear analyses of composite laminates. A finite element idealization with a four‐noded linear and a nine‐noded quadrilateral isoparametric elements, both belonging to the Lagrangian family are used in space discretization. An explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices. The accuracy of the formulation is then established by comparing the presnt pseudo‐transient analysis results with the present static Newton‐Raphson method results and other available analytical closed‐form two dimensional and finite element solutions. The usefulness and effectiveness of this approach is established by comparing computational time required by this approach and Newton‐Raphson's approach.
TL;DR: In this paper, a simple estimate of the accuracy of the widely used Geckeler approximation for the axisymmetric bending of non-shallow spherical shells is presented, based on the edge deformation coefficients associated with a pair of arbitrary edge loadings, independent of the actual surfaceloading and edge conditions of a practical shell.
Abstract: A simple estimate of the accuracy of the widely‐used Geckeler approximation for the axisymmetric bending of non‐shallow spherical shells is presented. Based on the edge‐deformation coefficients associated with a pair of arbitrary edge loadings, this estimate is independent of the actual surface‐loading and edge conditions of a practical shell. In this respect, the note complements the findings of an earlier error study, which was based on specific surface loadings and boundary conditions. The complementary nature of the work lies in its use for providing (in the absence of more specialised results) a reasonable assessment of the accuracy of the Geckeler approximation for any loading and/or boundary conditions.
TL;DR: A triangular composite element with 15 degrees of freedom is introduced and it is shown that after an appropriate modification of the Zlamal coordinate transformation this element can be employed as a reference element to curvilinear triangular element of class C with nine degrees offreedom.
Abstract: A triangular composite element with 15 degrees of freedom is introduced. It is shown that after an appropriate modification of the Zlamal coordinate transformation this element can be employed as a reference element to curvilinear triangular element of class C with nine degrees of freedom. A complete list of the basis functions, together with a procedure for their automatic generation are included.