Papers by Klaus-jürgen Bathe
Nonlinear dynamic finite element analysis of pipe whip problems
Nichtlineare Finite-Elemente-Berechnungen in der Festkörper-und Strukturmechanik
Lösung von Bewegungsgleichungen in kinetischen Berechnungen
Springer eBooks, 2002
Implementierung der Finite-Elemente-Methode
Springer eBooks, 2002
An enhancement of overlapping finite elements
Computers & Structures, Feb 1, 2022
Computers & Structures, Oct 1, 2021
The objective of this paper is to identify the optimal load selection at the intermediate time po... more The objective of this paper is to identify the optimal load selection at the intermediate time point of the q 1 -Bathe time integration method. We study the truncation errors of the scheme in homogeneous and forced responses for various parameters. The optimal load at the sub-step is determined by minimizing the global truncation errors of forced responses. A numerical impulse analysis shows that the optimal load at the sub-step thus established actually corresponds to numerical impulses at the three-and four-point Newton-Cotes formulas for the second-and third-order accuracy cases, respectively. We illustrate the findings of our theoretical study in example solutions of two-dimensional structural dynamics and wave propagation problems. With the optimally selected load at the sub-step, more accurate solutions can be obtained in some analyses.
Some Results in the Analysis of Thin Shell Structures
Springer eBooks, 1981
This paper represents a progress report of some of the research that we are conducting in the fin... more This paper represents a progress report of some of the research that we are conducting in the finite element analysis of thin shell structures. We consider our isoparametric displacement-rotation thin shell element and our discrete-Kirchhoff-theory (DKT) plate/shell element, which we are continuously refining for accurate and effective geometric and materially nonlinear analysis. In the paper we briefly discuss the locking phenomenon of the isoparametric element, the use of this element as a transition element between shell surfaces and in shell-solid transitions, and we give some results using the DKT element.
Finite-Elemente-Methoden
Springer eBooks, 1986
SAP 4: A Structural Analysis Program for Static and Dynamic Response of Linear Systems
International Journal for Numerical Methods in Engineering, Dec 1, 1980
An assessment of flat triangular plate bending elements with displacement degrees-of-freedom at t... more An assessment of flat triangular plate bending elements with displacement degrees-of-freedom at the three comer nodes only is presented, with the purpose of identifying the most effective for thin plate analysis. Based on a review of currently available elements, specific attention is given to the theoretical and numerical evaluation of three triangular 9 degrees-of-freedom elements; namely, a discrete Kirchhoff theory (DKT) element, a hybrid stress model (HSM) element and a selective reduced integration (SRI) element. New and efficient formulations of these elements are discussed in detail and the results of several example analyses are given. It is concluded that the most efficient and reliable three-node plate bending elements are the DKT and HSM elements. 1. A particular shell theory is used and discreti~,ed.'*~ 2. Three-dimensional continuum equations are used and discretized (isoparametric elements) (References 6 and 7, etc.). 3. Plate bending and membrane element stiffnesses are superimposed and assembled in a global co-ordinate system (References 8 and 9, etc.). The three approaches have advantages and disadvantages, and it is still difficult to state which of the three approaches is most effective based on criteria combining accuracy, computational cost and simplicity in use (in the data input phase as well as in the interpretation of results). Approach 3 received a great deal of attention for the linear analysis of shell structures in the mid-l960s," but the activities related to approaches 1 and 2 have dominated the past 10 years. It is only recently that a new impetus has been given to the analysis of shells using approach 3.
On the Analysis of Creep Stability and Rupture
Elsevier eBooks, 1983
Abstract The analysis of problems involving creep material failure and creep buckling is consider... more Abstract The analysis of problems involving creep material failure and creep buckling is considered. Creep buckling analyses are presented for some columns. A finite element creep rupture analysis of a rotating disc is performed and the results are compared with other solutions. Calculations are also reported for titanium notched tensile specimens and the numerical results are compared with experimental creep investigations, in which micrographs have been taken to study the rupture mechanisms. All numerical solutions have been carried out using ADINA in which a creep-damage material law and the updated-Lagrangian-Jaumann formulation for the thermo-elastic-plastic and creep material model were implemented.
Some remarks and references on recent developments in finite element analysis procedures
Computers & Structures, 1991
Computers & Structures, Sep 1, 2016
The objective of this paper is to assess the reliability and effectiveness of the method of finit... more The objective of this paper is to assess the reliability and effectiveness of the method of finite spheres, a truly meshless overlapping finite element method, for the solution of practical three-dimensional linear elasticity problems. Advantages include simplified discretization and the elimination of element distortion. The method is implemented in the ADINA finite element program through a user-supplied element subroutine. The solutions of three increasingly complex three-dimensional problems are studied (1) to establish the reliability of the method for practical linear elasticity problems and (2) to assess the effectiveness of the method as compared to the standard finite element method. The solutions indicate that the method of finite spheres is between one and two orders of magnitude more expensive in computational time than the standard finite element method. This is still a promising result since there are significant time savings for the method of finite spheres during the pre-processing phase, particularly in the discretization of complicated three-dimensional geometries and because the overlapping sphere elements can be directly coupled to traditional finite elements.
Studies of finite element proceduresan evaluation of preconditioned iterative solvers
Computers & Structures, 1989
Abstract In this paper we study the use of conjugate gradient iterative solution techniques for t... more Abstract In this paper we study the use of conjugate gradient iterative solution techniques for the solution of sparse systems of algebraic equations generated by the problem ADINA [K.J. Bathe, Nucl. Engng Des . 98 , 57–67 (1986)], as well as those resulting from a finite element discretization of fluid flow problems. The symmetric positive definite systems generated by ADINA for static structural analysis are solved with a conjugate gradient iterative method with incomplete Cholesky preconditioning. A biconjugate gradient method is used with incomplete LU factorization as a preconditioner to solve the equations with nonsymmetric coefficient matrices arising in the analysis of a fluid flow problem. The results of our numerical experiments show that preconditioned iterative methods can have significant advantages over direct methods in the solution of large, sparse systems of equations arising in 3D static structural analysis. However, the equations arising in fluid flow analysis are not as amenable to iterative solution techniques of the kind described in this paper.
Thermo-elastic-plastic and creep analysis of shell structures
Computers & Structures, 1987
Computers S Structures Vol. 26. No. 1/2, pp. 135-143, 1987 Primed in Cr ai Britain. 0045.7949/87 ... more Computers S Structures Vol. 26. No. 1/2, pp. 135-143, 1987 Primed in Cr ai Britain. 0045.7949/87 $3.00+0.00 Pcrgiroon Journall Ltd. THERMO-ELASTIC-PLASTIC AND CREEP ANALYSIS OF SHELL STRUCTURES MiLOa KoJief and KLAUS-J RGEN BATHE + ...
Computers & Structures, Apr 1, 2020
The objective of this paper is to investigate the optimal use of some time integration schemes fo... more The objective of this paper is to investigate the optimal use of some time integration schemes for the solution of transient wave propagation problems. We study the accuracy characteristics of the trapezoidal rule and the q 1 -Bathe scheme considering various parameter sets ðq 1 ; c; CFLÞ with both consistent and lumped mass matrices. The q 1 -Bathe scheme includes also the standard-, b 1 =b 2 -Bathe methods, the Newmark method and the trapezoidal rule. The study of the numerical dispersion shows that in the case of the consistent mass matrix, the q 1 -Bathe scheme with a proper setting of ðq 1 ; cÞ and standard Bathe scheme provide similar dispersion errors and outperform the trapezoidal rule. The optimal CFL number of the q 1 -Bathe scheme is about 25% larger than for the standard Bathe scheme. In addition, we show that using a lumped mass matrix and proper values of q 1 < 0, c and CFL in the q 1 -Bathe scheme, more accurate solutions can be obtained in some analyses.
Nuclear Engineering and Design, Nov 1, 1974
Wiley Encyclopedia of Computer Science and Engineering, Jun 13, 2008
This online document is based on the lecture notes developed by the author since 1997 for the und... more This online document is based on the lecture notes developed by the author since 1997 for the undergraduate course on the FEM in the mechanical engineering department at the University of Cincinnati. Since this is an e-book, the author suggests that the readers keep it that way and view it either online or offline on his/her computer. The contents and styles of these notes will definitely change from time to time, and therefore hard copies may become obsolete immediately after they are printed. Readers are welcome to contact the author for any suggestions on improving this e-book and to report any mistakes in the presentations of the subjects or typographical errors. The ultimate goal of this ebook on the FEM is to make it readily available for students, researchers and engineers, worldwide, to help them learn subjects in the FEM and eventually solve their own design and analysis problems using the FEM. The author thanks his former undergraduate and graduate students for their suggestions on the earlier versions of these lecture notes and for their contributions to many of the examples used in the current version of the notes.
Formulierung und Berechnung von isoparametrischen Finite-Elemente-Matrizen
Springer eBooks, 1986
Uploads
Papers by Klaus-jürgen Bathe