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The purpose of this paper is to present eight local elasto‐plastic beam element formulations incorporated into the corotational framework for two‐noded three‐dimensional…
The purpose of this paper is to present eight local elasto‐plastic beam element formulations incorporated into the corotational framework for two‐noded three‐dimensional beams. These formulations capture the warping torsional effects of open cross‐sections and are suitable for the analysis of the nonlinear buckling and post‐buckling of thin‐walled frames with generic cross‐sections. The paper highlights the similarities and discrepancies between the different local element formulations. The primary goal of this study is to compare all the local element formulations in terms of accuracy, efficiency and CPU‐running time.
The definition of the corotational framework for a two‐noded three‐dimensional beam element is presented, based upon the works of Battini .The definitions of the local element kinematics and displacements shape functions are developed based on both Timoshenko and Bernoulli assumptions, and considering low‐order as well as higher‐order terms in the second‐order approximation of the Green‐Lagrange strains. Element forces interpolations and generalized stress resultant vectors are then presented for both mixed‐based Timoshenko and Bernoulli formulations. Subsequently, the local internal force vector and tangent stiffness matrix are derived using the principle of virtual work for displacement‐based elements and the two‐field Hellinger‐Reissner assumed stress variational principle for mixed‐based formulations, respectively. A full comparison and assessment of the different local element models are performed by means of several numerical examples.
In this study, it is shown that the higher order elements are more accurate than the low‐order ones, and that the use of the higher order mixed‐based Bernoulli element seems to require the least number of FEs to accurately model the structural behavior, and therefore allows some reduction of the CPU time compared to the other converged solutions; where a larger number of elements are needed to efficiently discretize the structure.
The paper reports computation times for each model in order to assess their relative efficiency. The effect of the numbers of Gauss points along the element length and within the cross‐section are also investigated.
The paper starts with a review of constitutive equations forrubber‐like materials, formulated in the invariants of the rightCauchy—Green deformation tensor. A general…
The paper starts with a review of constitutive equations for rubber‐like materials, formulated in the invariants of the right Cauchy—Green deformation tensor. A general framework for the derivation of the stress tensor and the tangent moduli for invariant‐based models, for both the reference and the current configuration, is presented. The free energy of incompressible rubber‐like materials is extended to a compressible formulation by adding the volumetric part of the free energy. In order to overcome numerical problems encountered with displacement‐based finite element formulations for nearly incompressible materials, three‐dimensional finite elements, based on a penalty‐type formulation, are proposed. They are characterized by applying reduced integration to the volumetric parts of the tangent stiffness matrix and the pressure‐related parts of the internal force vector only. Moreover, hybrid finite elements are proposed. They are based on a three‐field variational principle, characterized by treating the displacements, the dilatation and the hydrostatic pressure as independent variables. Subsequently, this formulation is reduced to a generalized displacement formulation. In the numerical study these formulations are evaluated. The results obtained are compared with numerical results available in the literature. In addition, the proposed formulations are applied to 3D finite element analysis of an automobile tyre. The computed results are compared with experimental data.
The boundary element method (BEM) and the finite element method (FEM) may be computationally expensive if complex problems are to be solved; thus there is the need of…
The boundary element method (BEM) and the finite element method (FEM) may be computationally expensive if complex problems are to be solved; thus there is the need of implementing them on fast computer architectures, especially parallel computers. Because these methods are complementary to each other, the coupling of FEM and BEM is widely used. In this paper, the coupling of displacement‐based FEM and collocation BEM and its implementation on a distributed memory system (Parsytec MultiCluster2) is described. The parallelization is performed by data partitioning which leads to a very high efficiency. As model problems, we assume linear elasticity for the boundary element method and elastoplasticity for the finite element method. The efficiency of our implementation is shown by various test examples. By numerical examples we show that a multiplicative Schwarz method for coupling BEM with FEM is very well suited for parallel implementation.
A mixed approach to large strain elastoplastic problems is presented in a somewhat different way to that usually used within the context of the additive split of the rate…
A mixed approach to large strain elastoplastic problems is presented in a somewhat different way to that usually used within the context of the additive split of the rate of deformation tensor into an elastic and plastic part. A non‐linear extended mixed variational equation, in which the Jacobian of the deformation gradient and the pressure part of the stress tensor appear as additional independent variables, is introduced. This equation is then linearized in the accordance with the Newton‐Raphson method to obtain the system of linear equations which represent the basis of the mixed finite element procedure. For the case of a bilinear isoparametric interpolation of the displacement field, and for piece‐wise constant pressure and Jacobian, simplified expressions, differing from similar expressions corresponding to mixed finite element implementations, are obtained. The effectiveness of the proposed mixed approach is demonstrated by means of two examples.
Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…
Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.
The objective of this work is to develop an element technology to recover the plane stress response without any plane stress specific modifications in the large strain…
The objective of this work is to develop an element technology to recover the plane stress response without any plane stress specific modifications in the large strain regime. Therefore, the essential feature of the proposed element formulation is an interface to arbitrary three‐dimensional constitutive laws. The easily implemented and computational cheap four‐noded element is characterized by coarse mesh accuracy and the satisfaction of the plane stress constraint in a weak sense. A number of example problems involving arbitrary small and large strain constitutive models demonstrate the excellent performance of the concept pursued in this work.
We compare potential‐based (ø‐U‐P0) and displacement‐based finite element methods for static analysis of contained fluids. A general transient formulation may be…
We compare potential‐based (ø‐U‐P0) and displacement‐based finite element methods for static analysis of contained fluids. A general transient formulation may be specialized to static analysis in both cases. In the potential‐based method velocity potentials (ø) and a single pressure (P0) variable are the unknowns in the fluid region. Displacements are the unknowns in the fluid for displacement‐based methods. Higher‐order displace‐ment‐based elements may produce singular matrices for some static analyses, restricting us to four‐node elements for reliability. While both methods can yield excellent results when compared with experimental data, potential‐based methods appear to have computational advantages over displacement‐based methods.
As far as steel‐rod structures are concerned the yield‐hinge theory is a very efficient approach of the ultimate‐load theory. Unfortunately, most of the published…
As far as steel‐rod structures are concerned the yield‐hinge theory is a very efficient approach of the ultimate‐load theory. Unfortunately, most of the published strategies suffer from considerable deficiencies which depend on two main reasons: first, the yield condition is not approximated very well, and, second, a flow rule is not incorporated at all. This may significantly affect the calculated load‐carrying behaviour and as a consequence the elasto‐plastic failure prediction. In the present paper a consistent formulation of a refined numerical method based on the yield‐hinge theory is consistently developed from the theory of plasticity. The derivation is carried out in the framework of a geometrically nonlinear Timoshenko beam theory discretized for the displacement based finite element method. The plastic deformations can be interpreted as three‐dimensional eccentric yield‐hinges (generalized yield‐hinges). The presented numerical xamples show the efficiency of the proposed method.
This paper, which is concerned with fluid‐structure interactionanalysis, is a sequel to our earlier paper which gave an introduction to thenumerical treatment of such…
This paper, which is concerned with fluid‐structure interaction analysis, is a sequel to our earlier paper which gave an introduction to the numerical treatment of such systems. The paper is divided into five main sections. In the first two, a state‐of‐the‐art review on near‐field and far‐field fluid structure interaction is presented. In attempting to highlight where current research should be directed, only the most widely used computer codes are reviewed in the third section. Conclusions are presented in the fourth section.
This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a…
This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable mixed formulation for incompressible linear elasticity which circumvents the need to satisfy inf-sup condition.
Using the hybrid FE–meshfree method, the displacement and pressure are interpolated conveniently with the same order so that a continuous pressure field can be obtained with low-order elements. The multiscale variational principle is then introduced into the Galerkin form to obtain stable and convergent results.
The present method is capable of overcoming volume locking and does not exhibit unphysical oscillations near the incompressible limit. Moreover, there are no extra unknowns introduced in the present method because the fine-scale unknowns are eliminated using the static condensation technique, and there is no need to evaluate any user-defined stability parameter as the classical stabilization methods do. The shape functions constructed in the present model possess continuous derivatives at nodes, which gives a continuous and more precise stress field with no need of an additional smooth process. The shape functions in the present model also possess the Kronecker delta property, so that it is convenient to impose essential boundary conditions.
The proposed model can be implemented easily. Its convergence rates and accuracy in displacement, energy and pressure are even comparable to those of second-order mixed elements.