Showing papers in "Engineering Computations in 1991"
TL;DR: In this paper, the governing field equations are regularized by adding rotational degrees of freedom to the conventional translational degree of freedom, and the convergence of the load-deflection curve to a unique solution upon mesh refinement and a finite width of the localization zone is demonstrated.
Abstract: Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from pathological mesh‐dependence when strain‐softening models are employed in failure analyses. In this contribution the governing field equations are regularized by adding rotational degrees‐of‐freedom to the conventional translational degrees‐of‐freedom. This so‐called elasto‐plastic Cosserat continuum model, for which an efficient and accurate integration algorithm and a consistent tangent operator are also derived in this contribution, warrants convergence of the load—deflection curve to a unique solution upon mesh refinement and a finite width of the localization zone. This is demonstrated for an infinitely long shear layer and a biaxial test of a strain‐softening elasto‐plastic von Mises material.
511 citations
TL;DR: Several applications for 2D or axisymmetric elasticity problems of a method to control the quality of a finite element computation, and to optimize the choice of meshes are presented.
Abstract: We present several applications for 2D or axisymmetric elasticity problems of a method to control the quality of a finite element computation, and to optimize the choice of meshes. The method used, which is very general, is based (i) on the concept of error in constitutive relation and (ii) on explicit techniques to construct admissible fields. Illustrative examples are shown for several 2D or axisymmetric elements (3 or 6 node triangles, 4 or 8 node quadrilaterals). They have been achieved with our code ESTEREF, a post‐processor of error computation and mesh optimization which can be interfaced with any finite element code.
163 citations
TL;DR: Although Pascal and C have managed to seduce some programmers with their newer design, the majority of users still favours Fortran into which most of those new features are eventually incorporated.
Abstract: Undoubtedly, Fortran dominates the field of scientific computing from commercial packages to university programs. Although Pascal and C have managed to seduce some programmers with their newer design, the majority of users still favours Fortran into which most of those new features are eventually incorporated. The innovative programming tools offered by new languages have not been able to justify the time and cost required for the training of programmers and the porting of existent code.
41 citations
TL;DR: In this article, the performance of three-dimensional elements is investigated using a two-tiered strategy, where the ability of some linear and quadratic 3D elements to deform correctly under nearly isochoric conditions is estimated using the well-known constraint-counting method, in which the ratio of the number of degrees of freedom over number of kinematic constraints present in the finite element mesh is determined.
Abstract: A marked characteristic of rubber‐like materials is the nearly incompressible behaviour. This type of behaviour is best modelled by mixed finite elements with separate interpolation functions for the displacements and the pressure. In this contribution the performance of three‐dimensional elements is investigated using a two‐tiered strategy. First, the ability of some linear and quadratic three‐dimensional elements to deform correctly under nearly isochoric conditions is estimated using the well‐known constraint‐counting method, in which the ratio of the number of degrees‐of‐freedom over the number of kinematic constraints present in the finite element mesh is determined. Next, the performance of the elements is assessed by numerical simulations for three cuboidal rubber blocks with different shape factors. The results turn out to be quite sensitive with respect to the ratio of the number of degrees‐of‐freedom over the number of kinematic constraints, since too many pressure degrees‐of‐freedom make the element overstiff, while too few pressure degrees‐of‐freedom may cause the occurrence of spurious kinematic modes. This observation appears to be not only valid for the global structural behaviour, but also with respect to the specific parts in the structure, where the above‐mentioned ratio is different from the global number, e.g., in corners of the structure.
29 citations
TL;DR: A survey of period infinite element developments can be found in this article, where Bettess and Zienkiewicz used infinite elements for periodic wave problems, as stated in Part 1.
Abstract: Survey of period infinite element developments The first infinite elements for periodic wave problems, as stated in Part 1, were developed by Bettess and Zienkiewicz, the earliest publication being in 1975. These applications were of ‘decay function’ type elements and were used in surface waves on water problems. This was soon followed by an application by Saini et al., to dam‐reservoir interaction, where the waves are pressure waves in the water in the reservoir. In this case both the solid displacements and the fluid pressures are complex valued. In 1980 to 1983 Medina and co‐workers and Chow and Smith successfully used quite different methods to develop infinite elements for elastic waves. Zienkiewicz et al. published the details of the first mapped wave infinite element formulation, which they went on to program, and to use to generate results for surface wave problems. In 1982 Aggarwal et al. used infinite elements in fluid‐structure interaction problems, in this case plates vibrating in an unbounded fluid. In 1983 Corzani used infinite elements for electric wave problems. This period also saw the first infinite element applications in acoustics, by Astley and Eversman, and their development of the ‘wave envelope’ concept. Kagawa applied periodic infinite wave elements to Helmholtz equation in electromagnetic applications. Pos used infinite elements to model wave diffraction by breakwaters and gave comparisons with laboratory photogrammetric measurements of waves. Good agreement was obtained. Huang also used infinite elements for surface wave diffraction problems. Davies and Rahman used infinite elements to model wave guide behaviour. Moriya developed a new type of infinite element for Helmholtz problem. In 1986 Yamabuchi et al. developed another infinite element for unbounded Helmholtz problems. Rajapalakse et al. produced an infinite element for elastodynamics, in which some of the integrations are carried out analytically, and which is said to model correctly both body and Rayleigh waves. Imai et al. gave further applications of infinite elements to wave diffraction, fluid‐structure interaction and wave force calculations for breakwaters, offshore platforms and a floating rectangular caisson. Pantic et al. used infinite elements in wave guide computations. In 1986 Cao et al. applied infinite elements to dynamic interaction of soil and pile. The infinite element is said to be ‘semi‐analytical’. Goransson and Davidsson used a mapped wave infinite element in some three dimensional acoustic problems, in 1987. They incorporated the infinite elements into the ASKA code. A novel application of wave infinite elements to photolithography simulation for semiconductor device fabrication was given by Matsuzawa et al. They obtained ‘reasonably good’ agreement with observed photoresist profiles. Haggblad and Nordgren used infinite elements in a dynamic analysis of non‐linear soil‐structure interaction, with plastic soil elements. In 1989 Lau and Ji published a new type of 3‐D infinite element for wave diffraction problems. They gave good results for problems of waves diffracted by a cylinder and various three dimensional structures.
26 citations
TL;DR: In this paper, the state-of-the-art review of infinite elements for dynamic problems is presented, that is, those which change in time, and the necessary radiation conditions for such problems are summarized.
Abstract: This paper is concerned with infinite elements for dynamic problems, that is, those which change in time. It is a sequel to our earlier paper on static problems. The paper is in a number of sections. The first is an introduction. In the second the state‐of‐the‐art review of infinite elements is updated. In the third, ‘added mass’ type effects are considered. In the fourth, time dependent problems of the diffusion type, which only involve the first time derivative are considered. Wave problems are considered in the fifth and the necessary radiation conditions for such problems are summarized. Section six deals with dynamic problems of a repetitive nature, that is periodic or harmonic problems. In section seven completely transient problems are dealt with and some fundamental difficulties are noted. Conclusions are drawn in section eight.
23 citations
TL;DR: In this article, a technique for computing free surfaces by a steady state approach has been included in the hot rolling code ROLL3, along with applications to some simple rolling passes in particular when several potentially free surfaces exist.
Abstract: A technique for computing free surfaces by a steady state approach has been included in the hot rolling code ROLL3 It has been described in a previous paper, along with applications to some simple rolling passes In the present text, new developments are included to deal with more complex geometries, in particular when several potentially free surfaces exist The problem of contact with flanks of grooves is given special care Application to dog bone formation and flattening is presented Then a case with two free surfaces is computed and compared to experiments An application is then performed to beam roughing passes
22 citations
TL;DR: In this article, a plane joint or interface element suitable for implementation into a standard nonlinear finite element code is considered, where sliding of the joint is assumed to be governed by Coulomb friction, with a non-associated flow rule and no cohesion.
Abstract: The paper considers a plane joint or interface element suitable for implementation into a standard non‐linear finite element code. Sliding of the joint is assumed to be governed by Coulomb friction, with a non‐associated flow rule and no cohesion. The constitutive equations are formulated in a manner appropriate for a backward difference discretization in time along the path of loading. It is shown that the backward difference assumption can lead to an explicit formulation in which no essential distinction need be drawn between opening and closing of the joint and sliding when the joint is closed. However, an inherent limitation of the dilatant Coulomb model becomes evident; the final formulation is internally consistent but does not describe reversed shear displacement in a physically reasonable way. Explicit equations for the consistent tangent stiffness and for the corrector step (or return algorithm) of the standard Newton—Raphson iterative algorithm are given. The equations have been implemented as a user element in the finite element code ABAQUS, and illustrative examples are given.
15 citations
TL;DR: Based on the orthogonal approach for hybrid element methods, refined three-dimensional isoparametric hybrid hexahedral elements have been developed as mentioned in this paper, and the behaviour of the proposed models are discussed in respect of coordinate invariance, spurious zero energy modes and the ability to pass the patch test.
Abstract: Based on the orthogonal approach for hybrid element methods, refined three‐dimensional isoparametric hybrid hexahedral elements have been developed The behaviour of the proposed models are discussed in respect of coordinate invariance, spurious zero energy modes and the ability to pass the patch test By adopting the orthogonality of strain energy, the element stiffness matrix can be decomposed into a series of stiffness matrices in which the implementational effectiveness can be improved A number of examples is used to demonstrate the implementation efficiency, accuracy and distortion insensitivity of the proposed elements, and its capacity of handling nearly incompressible materials
9 citations
TL;DR: In this article, the authors present a specific method which allows the direct 3D analysis of reinforced concrete beams with a suitable numerical cost, and several numerical examples illustrate the effectiveness of the method.
Abstract: Simplified methods are often employed for the analysis of reinforced concrete beams (R‐C beams). A three‐dimensional problem (3D) is often transformed into a two‐dimensional problem (2D) with some assumptions which are usually established in static. The essential reason for this simplification lies in the fact that the 3D finite element analysis is so expensive that it is impossible to study directly the non‐linear behaviour of R‐C beams in many cases. Our purpose is to present a specific method which allows the direct 3D analysis of R‐C beams with a suitable numerical cost. First, the 3D linear heterogeneous beam theory is briefly recalled as well as the continuum damage model used for concrete. Second, the non‐linear behaviour of concrete is introduced in the 3D beam theory. Several numerical examples illustrate the effectiveness of the method.
5 citations
TL;DR: In this paper, two analytical solutions of thermal problems connected with the disposal of nuclear waste are presented, and the use of the Kirchhoff transformation and the transformation of coordinates are made along with a numerical solution.
Abstract: Two analytical solutions of thermal problems connected with the disposal of nuclear waste are presented. Non‐linear diffusion problems are analysed. The use of the Kirchhoff transformation and the transformation of coordinates are made along with a numerical solution. Also comparison is made for the exact and numerical solutions for temperature histories at a nuclear waste site. A time dependent heat source is considered.
TL;DR: In this paper, a hybrid method based on three-dimensional finite element idealization in the near field and a semi-analytic scheme using the principles of wave propagation in multilayered half space in the far field is proposed for the dynamic soil-structure interaction analysis.
Abstract: A new hybrid method based on three‐dimensional finite element idealization in the near field and a semi‐analytic scheme using the principles of wave propagation in multilayered half space in the far field is proposed for the dynamic soil‐structure interaction analysis. The distinguishing feature of this technique from direct or indirect boundary integral techniques is that in boundary integral techniques a distribution of sources are considered at the near field boundary. Strengths of these sources are then adjusted to satisfy the continuity conditions across the near‐field/far‐field interface. In the proposed method unknown sources are placed not at the near field boundary but at the location of the structure. Then the Saint‐Venant's principle is utilized to justify that at a distant point the effect of the structure's vibration can be effectively modelled by an equivalent vibrating point force and vibrating moment at the structure's position. Thus the number of unknowns can be greatly reduced here. For soil‐structure interaction analysis by this method one needs to consider only three unknowns (two force components and one in‐plane moment) for a general two‐dimensional problem and six unknowns (three force components and three moment components) for a general three‐dimensional problem. When a vertically propagating elastic wave strikes a structure which is symmetric about two mutually perpendicular vertical planes the structure can only vibrate vertically for dilatational waves and horizontally for shear waves. Under this situation the number of unknowns is reduced to only one whereas in boundary integral and boundary element techniques the number of unknowns is dependent on the number of nodes at the near field boundary, which is generally much greater than six. Several example problems are solved in this paper using this technique for both flexible and rigid structures in multilayered soil media.
TL;DR: In this article, two methods of penalty factor computations in penalty contact algorithms are presented for axisymmetric tube expansion and asymmetric slab bending, the material bulk constitutive equation being isotropic and elasto-plastic.
Abstract: Inside the finite element framework of LAGAMINE code, the contact conditions are introduced with specific two‐node interface elements and four‐node quadrangular elements or four‐node one point quadrature elements. A non‐associated flow rule is involved for sliding unilateral contact modelling. Two methods of penalty factor computations in the penalty contact algorithms are presented. These methods are then used for contact modelling of two isothermal examples: axisymmetric tube expansion and asymmetric slab bending, the material bulk constitutive equation being isotropic and elasto‐plastic.
TL;DR: For example, the authors showed that a n point Gauss-Legendre quadrature formula can integrate a 2n-1 order polynomial exactly, which is the secret of the finite element method.
Abstract: For those who are working with the finite element method, one may somehow wonder why a n point Gauss‐Legendre quadrature formula can integrate a 2n—1 order polynomial exactly. The purpose of this note is to unravel the secret.
TL;DR: In this paper, a local equivalent linearization methodology is proposed to simulate nonlinear shock absorbers and dual-phase dampers in the convenient frequency domain, based on the principle of energy similarity, characterizes the nonlinear dual phase dampers via an array of local damping constants as function of local excitation frequency and amplitude, response, and type of nonlinearity.
Abstract: A local equivalent linearization methodology is proposed to simulate non‐linear shock absorbers and dual‐phase dampers in the convenient frequency domain The methodology based on principle of energy similarity, characterizes the non‐linear dual‐phase dampers via an array of local damping constants as function of local excitation frequency and amplitude, response, and type of non‐linearity The non‐linear behaviour of the dual‐phase dampers can thus be predicted quite accurately in the entire frequency range The frequency response characteristics of a vehicle model employing non‐linear dual‐phase dampers, evaluated using local linearization algorithm, are compared to those of the non‐linear system, established via numerical integration, to demonstrate the effectiveness of the algorithm An error analysis is performed to quantify the maximum error between the damping forces generated by non‐linear and locally linear simulations The influence of damper parameters on the ride improvement potentials of dual‐phase dampers is further evaluated using the proposed methodology and discussed
TL;DR: In this article, a trilinear eight-noded isoparametric fluid element with pressure variable as unknown is coupled to a nine−noded degenerate shell element.
Abstract: Three‐dimensional transient analysis of a submerged cylindrical shell is presented. Three‐dimensional trilinear eight‐noded isoparametric fluid element with pressure variable as unknown is coupled to a nine‐noded degenerate shell element. Staggered solution scheme is shown to be very effective for this problem. This allows significant flexibility in selecting an explicit or implicit integrator to obtain the solution in an economical way. Three‐dimensional transient analysis of the coupled shell fluid problem demonstrates that inclusion of bending mode is very important for submerged tube design—a factor which has not received attention, since most of the reported results are based on simplified two‐dimensional plane strain analysis.
TL;DR: In this article, an exact multiple-level dynamic substructure technique was developed by a combination of WYD algorithm and static multiplelevel substructuring technique, which is essentially different from the traditional mode component synthesis.
Abstract: An exact multiple‐level dynamic substructure technique was developed by a combination of WYD algorithm and static multiple‐level substructuring technique. This method is essentially different from the traditional mode component synthesis. The eigenvalues and eigenvectors created by the method are the eigenpairs for the whole structure and not for the components of structure. On the other hand, the dynamic response by using mode superposition can also be implemented in substructure level. This algorithm actually is an exact substructuring technique which means that substructuring itself did not introduce any additional error except the round‐off when a structure was split into some arbitrary subdomains and the error of WYD or mode superposition themselves. It is no longer necessary to assume any connective condition on the interface between substructures. This method makes the capacity of dynamic analysis of a structural analysis program unlimited. It is especially attractive for the programs on microcomputers. Of course, the method leads to a frequent I/O for a subsequent search of the files from each substructure. It is time consuming compared to the mode component synthesis. But the potential still exists to improve the efficiency by using parallel computation on concurrent computers. In this paper the theory and procedure of the algorithm are presented.
TL;DR: In this paper, a finite element formulation for flexure of isotropic plates based on a recent refined theory is developed, which incorporates effects of transverse shear, transverse normal stress and transverse normals.
Abstract: A finite element formulation for flexure of isotropic plates based on a recent refined theory is developed. The refined theory incorporates effects of transverse shear, transverse normal stress and transverse normal strain. The Galerkin finite element method was used to develop the finite element equations for both plate bending and inplane problems. The performance of the proposed finite element model was evaluated by solving problems of uniformly loaded thick plates with different support conditions. The results of the present formulation are compared with Mindlin/Reissner and elasticity solutions.
TL;DR: In this article, the Euler beam theory is used to study the dynamic stability of a composite material slider-crank mechanism with an elastic connecting rod, and the Ritz finite element procedure is applied to derive the governing equations of motion of the mechanism.
Abstract: The Euler beam theory is used to study the dynamic stability of a composite material slider‐crank mechanism with an elastic connecting rod. The Ritz finite element procedure is applied to derive the governing equations of motion of the mechanism. Based on the assumption that the slider‐crank mechanism is subjected to a sinusoidal input torque and the operation condition is at a steady dynamic state, the governing equations represent a system of second order differential equations with periodic coefficients of the Mathieu‐Hill type. Making use of the Bolotin method, the boundaries between stable and unstable solutions of the elastic connecting rod are constructed. The advantages of using composite materials in the design of mechanisms are demonstrated.
TL;DR: Using the Heaviside operator, a single partial differential equation is obtained for the space-time variation of the pore pressure in two adjacent soil layers undergoing simultaneous consolidation in this article, where a closed form expression for the solution to the problem is given as a generalized Fourier series.
Abstract: Using the Heaviside operator, a single partial differential equation is obtained for the space‐time variation of the pore pressure in two adjacent soil layers undergoing simultaneous consolidation. A closed form expression for the solution to the problem is given as a generalized Fourier series. The coordinate functions of the series are the eigenfunctions of the composite medium obtained computationally through the application of the extended Galerkin method.
TL;DR: This paper describes the addition of the time‐dependent terms to one such segregated solution scheme that solves the Navier—Stokes equations with finite difference and finite volume solution schemes.
Abstract: To‐date, several segregated finite element algorithms have been proposed that solve the Navier—Stokes equations. These have considered only steady‐state cases. This paper describes the addition of the time‐dependent terms to one such segregated solution scheme. Several laminar flow examples have been computed and comparisons made to predictions obtained with both finite difference and finite volume solution schemes. The finite element results compare very well with the results from the other schemes, both in terms of accuracy and the qualitative behaviour of the iterative schemes.
TL;DR: In this paper, an algorithm to calculate shape function values at specific points is presented, which applies to three-dimensional serendipity elements with variable node numbers per side and, as a particular case, to plane and truss elements.
Abstract: An algorithm to calculate shape function values at specific points is presented. It applies to three‐dimensional serendipity elements with variable node numbers per side and, as a particular case, to plane and truss elements. The procedure is shown for the two‐dimensional case using the natural orthogonal reference system of the element and is then generalized to the three‐dimensional case. The source code of the described algorithms written in Fortran 77 is included.
TL;DR: In this paper, an analysis model for the elasto-viscoplastic analysis of continuous fiber-reinforced composite structures was developed for the analysis of unidirectional composite plates subjected to inplane loads.
Abstract: An analysis model has been developed for the elasto‐viscoplastic analysis of continuous fibre‐reinforced composite structures. Elastic deformation of fibre and elasto‐viscoplastic deformation of matrix are considered in the analysis model because the yield strength of matrix is, in general, substantially lower than that of fibre. A finite element formulation is derived for the proposed analysis model. If matrix is assumed homogeneous and isotropic, the von Mises yield criterion is used for viscoplastic yielding. As numerical examples, a parametric study has been performed for elasto‐viscoplastic analysis of unidirectional composite plates subjected to inplane loads.