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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.
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.
A stiffened shell element is presented for geometricallynon‐linear analysis of eccentrically stiffened shell structures.Modelling with this element is more accurate than…
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.
The numerical simulation of metal forming processes follows a highly non‐linear analysis where general aspects such as elastoplasticity, finite deformation and contact…
The numerical simulation of metal forming processes follows a highly non‐linear analysis where general aspects such as elastoplasticity, finite deformation and contact mechanics are combined. Approximated solutions obtained by finite element techniques require strong computational effort, that contradicts the need of interactive industrial applications. The first part of the work deals with the description of the main elements of the formulation, with attention to mathematical modelling and the approximating algorithms in the incremental iterative frame of non‐linear analysis, ending with the results obtained in hot rolling simulation. The second part is dedicated to computational efficiency analysis and the presentation of the related methods and results obtained in this work.
This paper considers the extension of the force-based element formulation to simulate the nonlinear, temperature-dependent response of structural frames exposed to fire…
This paper considers the extension of the force-based element formulation to simulate the nonlinear, temperature-dependent response of structural frames exposed to fire. The two-dimensional formulation presented here accounts for thermal expansion, temperature-dependent material properties, and residual stresses. The element utilizes a fiber discretization to simulate the gradual plastification of the section. Geometric nonlinearities are included through coordinate transformations of the corotational reference frame. Analyses of benchmark experimental tests demonstrate that the force-based element formulation is computationally stable and provides accurate results for structures exposed to fire. In addition, comparisons to traditional displacement-based elements indicate that the force-based element may offer improved computational efficiency because fewer elements are needed per member.
A non‐linear shallow thin shell element is described. The element is a curved quadrilateral one with corner nodes only. At each node, six degrees of freedom (i.e. three…
A non‐linear shallow thin shell element is described. The element is a curved quadrilateral one with corner nodes only. At each node, six degrees of freedom (i.e. three translations and three rotations) make the element easy to connect to space beams, stiffeners or intersecting shells. The curvature is dealt with by Marguerre's theory. Membrane bending coupling is present at the element level and improves the element behaviour, especially in non‐linear analysis. The element converges to the deep shell solution. The sixth degree of freedom is a true one, which can be assimilated to the in‐plane rotation. The present paper describes how overstiffness due to membrane locking on the one hand and to the sixth degree of freedom on the other hand can be corrected without making use of numerical adjusted factors. The behaviour of this new element is analysed in linear and non‐linear static and dynamic tests.
The purpose of this paper is to describe several novel techniques for implementing a crystal plasticity (CP) material model in a large deformation, implicit finite element…
The purpose of this paper is to describe several novel techniques for implementing a crystal plasticity (CP) material model in a large deformation, implicit finite element framework.
Starting from the key kinematic assumptions of CP, the presentation develops the necessary CP correction terms to several common objective stress rates and the consistent linearization of the stress update algorithm. Connections to models for slip system hardening are isolated from these processes.
A kinematically consistent implementation is found to require a correction to the stress update to include plastic vorticity developed by slip deformation in polycrystals. A simpler, more direct form for the algorithmic tangent is described. Several numerical examples demonstrate the capabilities and computational efficiency of the formulation.
The implementation assumes isotropic slip system hardening. With simple modifications, the described approach extends readily to anisotropic coupled or uncoupled hardening functions.
The modular formulation and implementation support streamlined development of new models for slip system hardening without modifications of the stress update and algorithmic tangent computations. This implementation is available in the open-source code WARP3D.
In the process of developing the CP formulation, this work realized the need for corrections to the Green-Naghdi and Jaumann objective stress rates to account properly for non-zero plastic vorticity. The paper describes fully the consistent linearization of the stress update algorithm and details a new scheme to implement the model with improved efficiency.
A finite element procedure is presented for refined transient analysis of two‐dimensional (plane or axisymmetric) non‐linear structures involving arbitrarily large…
A finite element procedure is presented for refined transient analysis of two‐dimensional (plane or axisymmetric) non‐linear structures involving arbitrarily large displacements, rotations and strains. The finite element model is based on the biquadratic nine‐node element of the Lagrange family. The relevant points pertaining to the equations of motion and their integration and to the spatial description, including geometrical and material non‐linearities, are considered. In particular, stress and strain rates are discussed. Finally, significant numerical applications show the effectiveness of the proposed method.
Investigates the effects of two‐phase instability on finite element (FE) solutions for porous hypoelastic solids saturated with an insterstitial fluid. Demonstrates that…
Investigates the effects of two‐phase instability on finite element (FE) solutions for porous hypoelastic solids saturated with an insterstitial fluid. Demonstrates that two‐phase instability creates definite problems to the FE computations of coupled solid‐fluid systems. The eigenvectors of the tangential finite element matrices which are responsible for problems are not artificial, but are the bifurcating modes of physical solutions. The investigation, although limited to the plane strain undrained compression of hypoelastic models, is relevant to the investigation of the two‐phase instability of other materials and boundary value problems, and may lead towards an explanation for numerical problems in soil liquefaction analysis.
The numerical simulation of metal forming processes approximated by means of finite element techniques, require large computational effort, which contradicts the need of…
The numerical simulation of metal forming processes approximated by means of finite element techniques, require large computational effort, which contradicts the need of interactivity for industrial applications. This work analyses the computational efficiency of algorithms combining elastoplasticity with finite deformation and contact mechanics, and in particular, the optimum solution of the linear systems to be solved through the incremental‐iterative schemes associated with non linear implicit analysis. A method based on domain decomposition techniques especially adapted to contact problems is presented, as well as the improved performance obtained in the application to hot rolling simulation, as a consequence of bandwidth reduction and the differentiated treatment of subdomains along the non linear analysis.