Showing papers in "Engineering Computations in 1995"
TL;DR: In this paper, the authors discuss the issues involved in the development of combined finite/discrete element methods, both from a fundamental theoretical viewpoint and some related algorithmic considerations essential for the efficient numerical solution of large scale industrial problems.
Abstract: This paper discusses the issues involved in the development of combined finite/discrete element methods; both from a fundamental theoretical viewpoint and some related algorithmic considerations essential for the efficient numerical solution of large scale industrial problems. The finite element representation of the solid region is combined with progressive fracturing, which leads to the formation of discrete elements, which may be composed of one or more deformable finite elements. The applicability of the approach is demonstrated by the solution of a range of examples relevant to various industrial sections.
586 citations
TL;DR: An algorithm for contact resolution that is valid for a wide variety of polygonal two dimensional shapes and is of linear computational complexity and is designed for use in discrete element analysis of granular and multibody systems exhibiting discontinuous behaviour is presented.
Abstract: We present an algorithm for contact resolution that is valid for a wide variety of polygonal two dimensional shapes and is of linear computational complexity. The algorithm is designed for use in discrete element analysis of granular and multibody systems exhibiting discontinuous behaviour. Contact detection usually consists of a spatial sorting phase and a contact resolution phase. The spatial sorting phase seeks to avoid an all‐to‐all body comparison by culling the number of objects which are potential contactors of a given object. The contact resolution phase resolves the details of the contact between two given objects. The algorithm presented here (called DFR) addresses the contact resolution phase and is applicable to convex geometries and to a restricted set of concave geometries. Examination of the algorithm establishes an upper bound linear computational complexity, of order O(N), with respect to the number of points (N) used to define the object boundary. The DFR algorithm is combined with a modified heapsort algorithm for spatial sorting of M bodies which has complexity O(M log M) and is applied to a baseline granular simulation problem to test its efficiency.
131 citations
TL;DR: In this paper, the authors present the results of a Discrete Element Method study on the influence of particle shape on the strength and deformation behavior of two dimensional assemblages of ellipse-shaped particles.
Abstract: This paper presents the results of a Discrete Element Method study on the influence of particle shape on the strength and deformation behaviour of two dimensional assemblages of ellipse‐shaped particles. Assemblages of particles with varying individual particle aspect ratio were formed with a preferred bedding plane, isotropically compressed with varying isotropic confining stresses and then sheared with biaxial compression. The results indicate that Discrete Element analysis using two dimensional ellipse‐shaped particles produces mechanical behaviour which is similar both quantitatively and qualitatively to the behaviour of real granular materials. Even small particle out‐of‐roundness increases the observed macroscopic strength significantly. In systems composed of flatter particles, particle rotations are greatly inhibited. Decomposing relative contact displacements into contributions due to particle rotation and translation demonstrates that most of the displacements in round particle systems are due to individual particle rotation.
122 citations
TL;DR: In this article, an automated fully stressed design approach based on the Xie and Steven algorithm is presented, which is obtained by a gradual removal of low stressed material, by applying this evolutionary procedure a layout or topology of a structure can be found from an initial block of material.
Abstract: An automated fully stressed design approach based on the Xie and Steven algorithm is presented. With this algorithm a fully stressed design is obtained by a gradual removal of low stressed material. By applying this evolutionary procedure a layout or topology of a structure can be found from an initial block of material. A fully integrated, interactive program is presented which incorporates automatic mesh generation, finite element analysis and the fully stressed design algorithm. The feasibility of the approach is demonstrated using several examples.
108 citations
TL;DR: In this paper, a complete thermo-mechanical model for the simulation of the inertia welding process of two similar parts is described, where the material behaviour is represented by an incompressible viscoplastic Norton-Hoff law in which the rheological parameters are dependent on temperature.
Abstract: A complete thermo‐mechanical model for the simulation of the inertia welding process of two similar parts is described. The material behaviour is represented by an incompressible viscoplastic Norton—Hoff law in which the rheological parameters are dependent on temperature. The friction law was determined experimentally and depends on the prescribed pressure and the relative rotating velocity between the two parts. The mechanical problem is solved considering the virtual work principle including inertia terms. The computation of the three components of the velocity field such as radial, longitudinal and rotational velocity, in an axisymmetric approximation allows to take into account the torsional effects. The domain is updated based on a Lagrangian formulation. The non‐linear heat transfer equation with boundary conditions (convection, radiation and friction flux) is solved separately for each time step. Error estimators on mechanical and thermal computation are devised to adapt the mesh in an automatic w...
70 citations
TL;DR: In this paper, the problem of determining the path of loads in plates with geometric discontinuities and in simple joints is addressed, and the theory associated with the determination of the load path is first introduced, and then integrated into a finite element package to provide pictorial contours.
Abstract: The determination of load paths is an essential element of structural design. Load paths provide insight into the way the structure is performing its prescribed function. They can also indicate possibilities for shape optimization and the effect of component modification or damage. They are relatively easy to define in simple structures such as trusses which comprise a finite number of clearly defined members which carry only axial load. The load path is given simply by tracing the higher axial loads through the structure. However, for continua such as plates or solids, there is currently no systematic procedure for determining the path of load from the point of application to the constrained boundaries. This paper addresses the problem of defining the path of loads in plates with geometric discontinuities and in simple joints. The theory associated with the determination of the load path is first introduced, and then integrated into a finite element package to provide pictorial contours.
50 citations
TL;DR: In this article, a 4-node flat shell quadrilateral finite element with 6 degrees of freedom per node, denoted QC5D•SA, is presented. The element is an assembly of a modification of the drilling degree of freedom membrane presented by Ibrahimbegovic et al., and the assumed strain plate element presented by Bathe and Dvorkin.
Abstract: A 4‐node flat shell quadrilateral finite element with 6 degrees of freedom per node, denoted QC5D‐SA, is presented. The element is an assembly of a modification of the drilling degree of freedom membrane presented by Ibrahimbegovic et al., and the assumed strain plate element presented by Bathe and Dvorkin. The part of the stiffness matrix associated with in—plane displacements and rotations is integrated over the element domain by a modified 5‐point reduced integration scheme, resulting in greater efficiency without the sacrifice of rank sufficiency. The scheme produces a soft higher order deformation mode which increases numerical accuracy. A large number of standard benchmark problems are analyzed. Some examples show that the effectiveness of a previously proposed “membrane locking correction” technique is significantly reduced when employing distorted elements. However, the element is shown to be generally accurate and in many cases superior to existing elements.
48 citations
TL;DR: In this article, a flexible boundary is proposed to analyze three-dimensional assemblies of spheres, composed of adjoining triangular plate elements which are connected at their corners to the centres of neighbouring spheres.
Abstract: An algorithm is presented for creating a flexible boundary to analyse three‐dimensional assemblies of spheres. It can be used to study localization phenomena in particulate materials. The boundary is composed of adjoining triangular plate elements which are connected at their corners to the centres of neighbouring spheres. The applied external boundary stresses create traction forces on the plates, which are distributed among the plates’ particles. The boundary performed favourably in tests on a large assembly of particles when only contact and rotational damping were used. Plane strain compression tests on assemblies with flexible and periodic boundaries revealed a lower strength with the former. This result could be due to the greater restraint on particle movements produced by periodic boundaries or to the early development of a column buckling failure pattern of the assembly with flexible boundaries. No shear bands were observed in the assembly.
47 citations
TL;DR: In this paper, a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials is presented, where the authors assume the existence of a real aisotropic space and other fictitious isotropics space where a mapped fictitious problem is solved.
Abstract: This paper shows a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials. This approach assumes the existence of a real anisotropic space, and other fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order transformation tensor that contains all the information concerning the real anisotropic material. The paper describes the basis of the spaces transformation proposed and the expressions of the resulting secant and tangent constitutive equations. Also details of the numerical integration of the constitutive equation are provided. Examples of application showing the good performance of the model for analysis of orthotropic materials and fibre‐reinforced composites are given.
46 citations
TL;DR: In this paper, a two dimensional finite element analysis is used to study the effect of localized end loads on micropolar solids in two-dimensional (2D) strip geometry.
Abstract: Distributions of stress and strain in composite and cellular materials can differ significantly from the predictions of classical elasticity. For example, concentration of stress and strain around holes and cracks is consistently less than classical predictions. Generalized continuum theories such as micropolar (Cosserat) elasticity offer improved predictive power. In this article Saint‐Venant end effects for self equilibrated external forces in micropolar solids are investigated in two dimensions. A two dimensional finite element analysis is used which takes into account the extra degrees of freedom, to treat the problem of localized end loads acting upon a strip. The rate of decay of strain energy becomes slower in a two dimensional strip as the micropolar characteristic length l is increased (for l sufficiently less than the strip width). For the strip geometry a Cosserat solid exhibits slower stress decay than a classical solid.
42 citations
TL;DR: In this article, the analysis of error estimation is addressed in the framework of viscoplasticity problems, this is to say, of incompressible and non-linear materials.
Abstract: The analysis of error estimation is addressed in the framework of viscoplasticity problems, this is to say, of incompressible and non‐linear materials. Firstly, Zienkiewicz—Zhu (Z2) type error estimators are studied. They are based on the comparison between the finite element solution and a continuous solution which is computed by smoothing technique. From numerical examples, it is shown that the choice of a finite difference smoothing method (Orkisz’ method) improves the precision and the efficiency of this type of estimator. Then a Δ estimator is introduced. It makes it possible to take into account the fact that the smoothed solution does not verify the balance equations. On the other hand, it leads us to introduce estimators for the velocity error according to the L2 and L∞norms, since in metal forming this error is as important as the energy error. These estimators are applied to an industrial problem of extrusion, demonstrating all the potential of the adaptive remeshing method for forming processes.
TL;DR: In this paper, the general problem of sizing, material and loading parameter sensitivity of nonlinear systems is presented, where both kinematic and path-dependent material nonlinearities are considered; nonlinear sensitivity path is traced by an incremental solution strategy.
Abstract: The general problem of sizing, material and loading parameter sensitivity of non‐linear systems is presented. Both kinematic and path‐dependent material non‐linearities are considered; non‐linear sensitivity path is traced by an incremental solution strategy. The variational approach employed is quite general and can be employed for studying sensitivity of various path‐dependent highly non‐linear phenomena. Both the direct differentiation method (DDM) and adjoint system method (ASM) are discussed in the context of continuum and finite element mechanics. The merits of using the consistent tangent matrix and the necessity of accumulation of design derivatives of stresses and internal parameters are indicated. Aspects of sensitivity problems in metal forming are also discussed. A number of examples illustrate the paper.
TL;DR: The modal damping factor is defined as the ratio of the strain energy dissipated per radian of vibration, in the mode of interest, to the total strain energy of the entire laminate at maximum displacement during the same cycle as mentioned in this paper.
Abstract: The present investigation is concerned with the utilisation of the finite element technique for predicting the natural frequencies and the modal damping factor (also called the loss factor) of anisotropic fibre‐reinforced composite laminated plates. The simple definition of the modal damping factor is defined as the ratio of the strain energy dissipated per radian of vibration, in the mode of interest, to the total strain energy of the entire laminate at maximum displacement during the same cycle. Results for the vibration and damping analysis of multi‐layered plates obtained by the present methods are compared with the results obtained by other authors and with the results of experiments.
TL;DR: In this paper, a generalized eigensystem approach and a modified generalized eigensystem approach were compared to more widely used truncated singular value decomposition and zero-order Tikhonov regularization for solving multidimensional elliptic inverse problems.
Abstract: We compare a recently proposed generalized eigensystem approach and a new modified generalized eigensystem approach to more widely used truncated singular value decomposition and zero‐order Tikhonov regularization for solving multidimensional elliptic inverse problems. As a test case, we use a finite element representation of a homogeneous eccentric spheres model of the inverse problem of electrocardiography. Special attention is paid to numerical issues of accuracy, convergence, and robustness. While the new generalized eigensystem methods are substantially more demanding computationally, they exhibit improved accuracy and convergence compared with widely used methods and offer substantially better robustness.
TL;DR: In this paper, the dispersive behavior of wave propagation in softening problems is analyzed and the influence of the numerical scheme on the dispersion characteristics in the process of localization of deformation is focused.
Abstract: The dispersive behaviour of waves in softening problems is analysed. Attention is focused on the influence of the numerical scheme on the dispersion characteristics in the process of localization of deformation. Distinction has been made between softening models defined in a standard plasticity framework and in a gradient‐dependent plasticity theory. Waves in a standard softening plasticity continuum do not disperse but due to spatial discretization dispersion is introduced which results in a mesh size dependent length scale effect. On the other hand, wave propagation in a gradient‐dependent softening plasticity continuum is dispersive. By carrying out the dispersion analysis on the discretized system the influence of numerical dispersion on material dispersion can be quantified which enables us to determine the accuracy for the solution of the localization zone. For a modelling with and without the inclusion of strain gradients accuracy considerations with respect to mass discretization, finite element s...
TL;DR: In this paper, the optimal design of composite laminated plates is analyzed using the constrained variable metric metric (CVM) and a finite element method, which is suitable for from thin to thick plates and includes the transverse shear effects.
Abstract: This paper deals with the optimum design of composite laminated plates. Both ply orientation angles and ply thicknesses of the composite plate are used as design variables. The optimum design process is divided into two sublevels. In the first sublevel, the strain energy of the plate is minimized by changing the ply orientation angles while the ply thickness distributions remain unmodified. In the second sublevel, with the angle values obtained in the first sublevel, the optimum thickness distribution of each ply is obtained by minimizing the structural weight while satisfying stiffness and gauge constraints. The final optimum design is achieved by iterating between these two sublevels. The stiffness analysis is performed by the finite element method in which a triangular element is used that is suitable for from thin to thick plates and includes the transverse shear effects. All the derivative analysis is performed analytically. The mathematical programming method called Constrained Variable Metric is used to solve the optimum problem. An example is provided for a rectangular laminated plate with good results to show the effectiveness of the method.
TL;DR: This article focuses on a contact updating problem that arises when a penalty based contact model is used and a simple yet effective scheme to overcome ambiguities is presented.
Abstract: The motion of systems of polygonal objects is characterized by discontinuities due to changes in the set of contacts between polygons. Effective simulations of such a motion requires a simulation scheme that can automatically update the set of contacts during the simulation. This article focuses on a contact updating problem that arises when a penalty based contact model is used. A penalty based model requires a finite overlap of contacting polygons. This overlap results in ambiguities in characterizing corner‐corner contact between polygons. A simple yet effective scheme to overcome such ambiguities is presented.
TL;DR: A damping scheme is proposed in order to achieve a stable solution procedure in dynamic sheet forming problems and BEAM (abbreviated from Bending Energy Augmented Membrane) elements, are employed.
Abstract: In the present work a rigid‐plastic finite element formulation using a dynamic explicit time integration scheme is proposed for numerical analysis of sheet metal forming processes. The rigid‐plastic finite element method, based on membrane elements, has long been employed as a useful numerical technique for the analysis of sheet metal forming because of its time effectiveness. The explicit scheme, in general, is based on the elastic‐plastic modelling of material requiring large computation time. The resort to rigid‐plastic modelling would improve the computational efficiency, but this involves new points of consideration such as zero energy mode instability. A damping scheme is proposed in order to achieve a stable solution procedure in dynamic sheet forming problems. In order to improve the drawbacks of the conventional membrane elements, BEAM (abbreviated from Bending Energy Augmented Membrane) elements, are employed. Rotational damping and spring about the drilling direction are introduced to prevent a...
TL;DR: In this paper, a finite element solution to the rolling of two-phase materials is presented and applied to a rolling of prepared sugar cane, where the generalized Biot theory is extended and modified to suit the present problem and the velocity of the solid skeleton and pore pressure are taken as the primary unknowns.
Abstract: A finite element solution to the rolling of two‐phase materials is presented and applied to the rolling of prepared sugar cane. The generalized Biot theory is extended and modified to suit the present problem and the velocity of the solid skeleton and the pore pressure are taken as the primary unknowns. The finite element approach is applied to the governing equations for spatial discretization, followed by time domain discretization by standard difference methods. A constitutive relation evaluated from a finite element simulation of experiments performed on a constrained compression test cell is employed. The computational model of the rolling of prepared cane with two rolls is presented. The material parameters of prepared cane are described and their variation during the rolling process are derived and discussed. Numerical results are presented to illustrate the performance and capability of the model and solution procedures.
TL;DR: In this article, a consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed based on an augmented Lagrangian approach coupled to an implicit quasi-static Finite Element Method.
Abstract: A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach coupled to an implicit quasi‐static Finite Element Method. Analogous to classical work hardening theory in elasto‐plasticity, the frictional work is chosen as the internal variable for formulating the evolution of the friction convex. In order to facilitate the implementation of a wide range of phenomenological models, the friction coefficient is defined in a parametrised form in terms of Bernstein polynomials. Numerical simulation of a 3D deep‐drawing operation demonstrates the performance of the methods for predicting frictional contact phenomena in the case of large sliding paths including high curvatures.
TL;DR: In this article, the assumed shear strain method in a novel finite rotation shell theory is discussed, and careful considerations of the pertinent aspects of the Newton solution procedure are given, which results in a very robust performance of the presented 4-node shell element in some challenging finite rotation problems.
Abstract: Implementation details of the assumed shear strain method in a novel finite rotation shell theory are discussed. Careful considerations of the pertinent aspects of the Newton solution procedure are given. The latter results in a very robust performance of the presented 4–node shell element in some challenging finite rotation problems.
TL;DR: In this article, a two-grid algorithm was proposed to solve frictional contact problems and a regularized formulation was introduced and the discretized problem was solved using an internal non-linear twogrid technique coupled with a diagonal fixed point algorithm.
Abstract: This paper is the description of a new two‐grid algorithm to solve frictional contact problems. A regularized formulation is introduced and the discretized problem is solved using an internal non linear two‐grid technique coupled with a diagonal fixed point algorithm. Mathematical background is given, and superconvergence is obtained.
TL;DR: In this article, the treatment of fluid-structure interaction problems is discussed in a number of sections and the main factors affecting the numerical treatment of these problems are identified, and the next eight sections discuss each of these factors separately.
Abstract: This paper is concerned with the treatment of fluid‐structure interaction problems. The paper is divided in a number of sections. The first is an introduction to the historical background which lead to the numerical approach being used today. In the second the main factors affecting the numerical treatment of fluid‐structure interaction problems are identified. The next eight sections discuss each of these factors separately. Conclusions are drawn in section eleven.
TL;DR: A finite element model for calculating the die temperature profile for a hot-forging operation is presented in this paper, where the workpiece is modelled as a thermo-viscoplastic material, while the dies are considered undeformable.
Abstract: A finite‐element model for calculating the die temperature profile for a hot‐forging operation is presented. The workpiece is modelled as a thermo‐viscoplastic material, while the dies are considered undeformable. Heat transfer between the dies and the workpiece is modelled using an iteratively coupled, fixed‐point calculation of the temperature in each domain. Transfer of temperature boundary conditions across contact interfaces is performed for non‐coincident meshes, using a boundary integration point contact analysis. Two industrial‐type examples are presented. In the first example, the effectiveness of the transfer of the temperature boundary conditions for a non steady‐state forging process is evaluated and determined to be satisfactory. Then weakly‐ and strongly‐coupled temperature resolutions are compared. It was found that the strongly‐coupled resolution may be necessary in order to obtain reasonably accurate results. In the second example, the weakly‐coupled resolution is compared to a constant‐temperature die approach for a relatively slow forging process, which shows the influence of the die temperature on the flow of the material.
TL;DR: A tailored graphical user interface for finite element analysis, fully integrated into Microsoft Windows 3.1, has been developed and the current application is the simulation of flat sheet extrusion of thermoplastics.
Abstract: A tailored graphical user interface (GUI) for finite element analysis, fully integrated into Microsoft Windows 3.1, has been developed. The current application is the simulation of flat sheet extrusion of thermoplastics, but many of the features would be common to a wide range of finite element analyses. Microsoft’s C/C++ Professional Development System 7.0, including the Software Development Kit 3.1 (SDK), has been used as the programming tool for the GUI. The interface is based on the Common User Access Advanced Interface Design Guide, which is part of the IBM Systems Application Architecture Library, and The Windows Interface: An Application Design Guide, which is part of the SDK. A memory handling technique is proposed to break the imposed 64 KB data segmentation. Connected finite element calculation routines are written in Fortran and compiled by the Salford FTN77/x86 32‐bit compiler. The protected mode interface of the Fortran compiler allows direct access by the GUI, and allows the computation to r...
TL;DR: In this article, the equation of motion of a beam on multiple supports, subject to prescribed time-dependent conservative axial loads, is formulated based on Hamilton's principle and the assumed mode method.
Abstract: The equation of motion of a beam on multiple supports, subject to prescribed time‐dependent conservative axial loads, is formulated based on Hamilton’s principle and the assumed mode method. The effects of sinusoidal perturbations in respect of the axial loads are then examined using Bolotin’s method. The respective regions of instability are determined by converting the resulting equations of boundary frequencies into the standard form of a generalized eigenvalue problem. Instability regions are presented for various combinations of support configuration, average value and amplitude of the sinusoidal perturbations of the axial loads.
TL;DR: In this article, an adaptive scheme to solve diffusion problems, using linear and quadratic triangles, is presented, based on the subdivision of the selected elements, and the error estimator used are described first.
Abstract: In this work an adaptive scheme to solve diffusion problems, using linear and quadratic triangles, is presented. The densification algorithm, based on the subdivision of the selected elements, and the error estimator used are described first. We pay special attention to the behaviour of the estimator. It has two contributions: the residual term and the flux‐jump term. Babuska and co‐workers have shown that for bilinear quadrilterals, the first term is negligible, but for biquadratic, it is the dominant term. We show evidence suggesting that these results cannot be extended to triangular elements when the problem has a singular solution. We found, in this case, that if the flux‐jump term is neglected, the expected rate of convergence cannot be obtained. Finally, some remarks about the whole adaptive process are discussed.
TL;DR: An automated design system for nuclear structural components under complicated loading conditions and a “design window” which designates a satisfaction area for all design criteria in a design variable space is described.
Abstract: This paper describes an automated design system for nuclear structural components under complicated loading conditions. As a basic strategy of designing structures considering various loading conditions, the “generate and test” strategy is adopted because of simplicity and broad applicability. The object‐oriented knowledge representation technique is adopted to store knowledge modules related to design problems, while the data‐flow processing technique is utilized as an inference mechanism among the knowledge modules. As efficient design modification mechanisms, the present system utilizes two approaches, (a) an empirical approach based on experts’ empirical knowledge and the fuzzy control, and (b) a mathematical approach based on numerical sensitivity analysis. Using the present system, one can also obtain a “design window” which designates a satisfaction area for all design criteria in a design variable space. The fundamental performances of this system are clearly demonstrated through the design of a t...
TL;DR: In this article, a stiffened shell element is presented for geometrically non-linear analysis of eccentrically stiffened shells, which is more accurate than with the traditional equivalent orthotropic plate element or with lumping stiffeners.
Abstract: A stiffened shell element is presented for geometrically non-linear analysis of eccentrically stiffened shell structures. Modelling with this element is more accurate than with the traditional equivalent orthotropic plate element or with lumping stiffeners. In addition, mesh generation is easier than with the conventional finite element approach where the shell and beam elements are combined explicitly to represent stiffened structures. In the present non-linear finite element procedure, the tangent stiffness matrix is derived using the updated Lagrangian formulation and the element strains, stresses, and internal force vectors are updated employing a corotational approach. The non-vectorial characteristic of large rotations is taken into account. This stiffened shell element formulation is ideally suited for implementation into existing linear finite element programs and its accuracy and effectiveness have been demonstrated in several numerical examples.
TL;DR: A two‐grid iterative method for 3D linear elasticity problems, discretized using quadratic tetrahedral elements is proposed, and the conjugate‐gradient method is used as smoother.
Abstract: A two‐grid iterative method for 3D linear elasticity problems, discretized using quadratic tetrahedral elements is proposed. The conjugate‐gradient method is used as smoother. As compared to the conjugate‐gradient alone, it is shown, via numerical examples, that the method is much more efficient on the basis of computing time and memory allocation. The convergence property of the method is sensitive to the regularity of the problem.