For the theory used in ADINA, for structural analysis, CFD, and FSI, and also for
the philosophy used in the program development, please refer to the publications given here:
For publications that reference the use of ADINA, please see here.
3D-shell elements for structures in large strains
Sussman, Theodore, and Bathe, Klaus-Jürgen. Source: Computers & Structures, In Press
Abstract: We present in this paper MITC shell elements for large strain solutions of shell structures. While we focus on the 4-node element, the same formulation is also applicable to the 3-node element. Since the elements are formulated using three-dimensional continuum theory with the full three-dimensional constitutive behavior, they are referred to as 3D-shell elements. Specific contributions in this paper are that the elements are formulated using two control vectors at each node to describe the large deformations, MITC tying and volume preserving conditions acting directly on the material fiber vectors to avoid shear locking, and a pressure interpolation to circumvent volumetric locking. Also, we present solutions to some large strain shell problems that represent valuable benchmark tests for any large strain shell analysis
capability.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Keywords:
Shell elements, 3D-shell elements, MITC tying, large strains, benchmark solutions, buckling
The finite element method enriched by interpolation covers
Kim, Jaehyung, and Bathe, Klaus-Jürgen. Source: Computers & Structures, v. 116, 35-49, 2013
Abstract: In this paper, we focus on an enriched finite element solution procedure for low-order elements based on the use of interpolation cover functions. We consider the 3-node triangular and 4-node tetrahedral displacement-based elements for two- and three-dimensional analyses, respectively. The standard finite element shape functions are used with interpolation cover functions over patches of elements to increase the convergence of the finite element scheme. The cover functions not only capture higher gradients of a field variable but also smooth out inter-element stress jumps. Since the order of the interpolations in the covers can vary, the method provides flexibility to use different covers for different patches and increases the solution accuracy without any local mesh refinement. As pointed out, the procedure can be derived from various general theoretical approaches and the basic theory has been presented earlier. We evaluate the effectiveness of the method, and illustrate the power of the scheme through the solution of various problems. The method also has potential for the development of error measures.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Keywords:
Enriched finite elements, 3-node 2D & 4-node 3D elements, cover functions, higher convergence, increase in accuracy, adaptive interpolation
A stress improvement procedure
Payen, Daniel Jose, and Bathe, Klaus-Jürgen. Source: Computers & Structures, v. 112-113, 311-326, 2012
Abstract: In this paper, we present a novel procedure to improve the stress predictions in static, dynamic and non-linear analyses of solids. We focus on the use of low-order displacement-based finite elements – 3-node and 4-node elements in two-dimensional (2D) solutions, and 4-node and 8-node elements in 3D solutions – because these elements are computationally efficient provided good stress convergence is
obtained. We give a variational basis of the new procedure and compare the scheme, and its performance, with other effective previously proposed stress improvement techniques. We observe that the stresses of the new procedure converge quadratically in 1D and 2D solutions, i.e. with the same order as the displacements, and conclude that the new procedure shows much promise for the analysis of solids, structures and multiphysics problems, to calculate improved stress predictions and to establish error measures.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Keywords:
Finite element stress calculation, low-order displacement-based elements, stress recovery, stress convergence, mixed method, error measures
The subspace iteration method – Revisited
Bathe, Klaus-Jürgen. Source: Computers & Structures, 10.1016/j.compstruct.2012.06.002
Abstract: The objective in this paper is to present some recent developments regarding the subspace iteration
method for the solution of frequencies and mode shapes. The developments pertain to speeding up the
basic subspace iteration method by choosing an effective number of iteration vectors and by the use of
parallel processing. The subspace iteration method lends itself particularly well to shared and distributed
memory processing. We present the algorithms used and illustrative sample solutions. The present paper
may be regarded as an addendum to the publications presented in the early 1970s, see Refs.[1,2], taking
into account the changes in computers that have taken place.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Keywords:
Frequencies, mode shapes, subspace iteration method, parallel processing, shared memory, distributed memory
Insight into an implicit time integration scheme for structural dynamics
Bathe, Klaus-Jürgen and Noh, Gunwoo. Source: Computers & Structures, v. 98-99, 1-6, 2012.
Abstract: In Refs. [1,2], an effective implicit time integration scheme was proposed for the finite element solution
of nonlinear problems in structural dynamics. Various important attributes were demonstrated. In particular,
it was shown that the scheme remains stable, without the use of adjustable parameters, when the commonly
used trapezoidal rule results in unstable solutions. In this paper we focus on additional important attributes of the
scheme, and specifically on showing that the procedure can also be effective in linear analyses. We give, in
comparison to other methods, the spectral radius, period elongation, and amplitude decay of the scheme and
study the solution of a simple ‘model problem’ with a very flexible and stiff response.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Keywords:
Structural dynamics, finite elements, implicit time integration, trapezoidal rule, Newmark method,
Bathe method
Crushing and crashing of tubes with implicit time integration
Kazanci, Zafer, and Bathe, Klaus-Jürgen. Source: International Journal of Impact Engineering, v. 42, 80-88, 2012.
Abstract: The axial crushing and crashing of thin-walled high-strength steel tubes is performed using 3D-shell
finite elements and an implicit time integration scheme. The calculated results are compared with
published experimental data and results obtained using explicit time integration. The objective is to
show that, while for such analyses generally explicit time integration is used, with the current state of
the art also an implicit time integration solution should be considered, and such solution approach can
provide an effective alternative for a simulation.
ISSN: 0734-743X
Publisher: Elsevier Ltd
Keywords:
Dynamic axial crushing, implicit time integration, Bathe method, 3D-shell element, crash tube
A finite element method enriched for wave propagation problems
Ham, Seounghyun, and Bathe, Klaus-Jürgen. Source: Computers & Structures, v. 94-95, 1-12, 2012.
Abstract: An enriched finite element method is presented to solve various wave propagation problems. The
proposed method is an extension of the procedure introduced by Kohno, Bathe, and Wright for one-dimensional
problems [1]. Specifically, the novelties are: two-dimensional problems are solved (and three-dimensional
problems would be tackled similarly), a scheme is given to overcome ill-conditioning, the method is presented
for time-dependent problems, and focus is on the solution of problems in solids and structures using real
arithmetic only. The method combines advantages of finite element and spectral techniques, but an important
point is that it preserves the fundamental properties of the finite element method. The general formulation of the
procedure is given and various examples are solved to illustrate the capabilities of the proposed scheme.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Keywords:
Wave propagation, finite elements, spectral methods, harmonics
Improved stresses for the 4-node tetrahedral element
Payen, Daniel Jose and Bathe, Klaus-Jürgen. Source: Computers & Structures, v. 89, 1265-1273, 2011.
Abstract: The objective in this paper is to present the method for the calculation of improved stresses published by Payen and Bathe in [1] for the 4-node three-dimensional tetrahedral element. This element is widely used
in engineering practice to obtain, in general, only ‘‘guiding’’ results in the analysis of solids because the
element is known to be poor in stress predictions. We show in this paper the potential of this novel
approach to significantly enhance the stress predictions with the 4-node tetrahedral element at a relatively
low computational cost.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Keywords:
Stress improvements, stress recovery, NPF-based stresses, nodal point forces, finite elements
4-Node tetrahedral element
Modeling large strain anisotropic elasto-plasticity with logarithmic strain and stress measures
Caminero, Miguel Ángel, Montáns, Francisco Javier and Bathe, Klaus-Jürgen. Source: Computers &
Structures, v. 89, 826-843, 2011.
Abstract: In this paper we present a model and a fully implicit algorithm for large strain anisotropic elasto-
plasticity with mixed hardening in which the elastic anisotropy is taken into account. The formulation is
developed using hyperelasticity in terms of logarithmic strains, the multiplicative decomposition of the
deformation gradient into an elastic and a plastic part, and the exponential mapping. The novelty in
the computational procedure is that it retains the conceptual simplicity of the large strain isotropic elasto-
plastic algorithms based on the same ingredients. The plastic correction is performed using a standard
small strain procedure in which the stresses are interpreted as generalized Kirchhoff stresses and the
strains as logarithmic strains, and the large strain kinematics is reduced to a geometric pre- and post-
processor. The procedure is independent of the specified yield function and type of hardening used, and for
isotropic elasticity, the algorithm of Eterovic and Bathe is automatically recovered as a special case. The
results of some illustrative finite element solutions are given in order to demonstrate the capabilities of
the algorithm.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Keywords:
Computational elasto-plasticity, large strains, logarithmic strains, hyperelasticity, mixed hardening
The MITC9 shell element in plate bending: mathematical analysis of a simplified case
Bathe, Klaus-Jürgen, Brezzi, Franco and Marini, L. Donatella. Source: Comput. Mech., v. 47, 617–626, 2011.
Abstract: We consider the 9-node shell element referred to as the MITC9 shell element in plate bending
solutions and present a simplified mathematical analysis. The element uses bi-quadratic interpolations of the
rotations and transverse displacement, and the “rotated Raviart-Thomas” interpolations for the transverse shear
stresses. A rigorous mathematical analysis of the element is still lacking, even for the simplified case of plate
solutions (that is, flat shells), although the numerical evidence suggests a good and reliable behavior.
Here we start such an analysis by considering a very simple particular case; namely, a rectangular plate,
clamped all around the boundary, and solved with a uniform decomposition. Moreover, we consider only the so-called limit case, corresponding to the limit equations that are obtained for the thickness t going to zero. While
the mathematical analysis of the limit case is simpler, such analysis, in general, gives an excellent indication of
whether shear locking is present in the real case t > 0. We detail that the element in the setting considered
shows indeed optimal behavior.
ISSN: 0178-7675
Publisher: Springer-Verlag
Keywords:
Plate, shell, shear locking, MITC9 shell element, convergence analysis
The use of nodal point forces to improve element stresses
Payen, Daniel Jose and Bathe, Klaus-Jürgen. Source: Computers & Structures, v. 89, 485-495, 2011.
Abstract:
We present in this paper a novel approach to stress calculations in finite element analysis. Rather than using the stress assumption employed in establishing the stiffness matrix, the element nodal point forces
are used, in a simple way, to enhance the finite element stress predictions at a low computational cost.
While this paper focuses on the improvement of the stress accuracy, the proposed procedure can also be
used as a basis for error estimation. Moreover, the procedure is quite general, and has the potential for
many applications in finite element analysis.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Keywords:
Stress improvements, stress recovery, nodal point forces, error estimation, finite elements
Measuring the convergence behavior of shell analysis schemes
Bathe, Klaus-Jürgen and Lee, Phill-Seung. Source: Computers & Structures, v. 89, 285-301, 2011.
Abstract:
While shells have been analyzed abundantly for many years in engineering and the sciences, improved finite element and related analysis methods are still much desired and researched. More general and
effective finite element procedures are needed for complex shell structures, including for the analysis
of composite shells and the optimization of shells. In this paper we discuss how finite element methods,
and other analysis techniques, should be tested in order to identify their reliability and effectiveness. We
summarize some important theoretical results, present appropriate test problems and convergence measures,
and we illustrate our discussion through some novel numerical results. An important conclusion is
that the testing has to be performed very carefully in order to obtain relevant results, and we show how
this is accomplished in detail.
ISSN: 0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Keywords:
Shells, finite element, convergence, benchmark problems
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