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:
You are welcome to download the second edition of the book, 4th printing, however, please note that the book is copyrighted and should only be used in the same manner as a purchased hardcopy of the book. Improved versions will be made available here, from time to time, as the 5th printing, and so on. "Finite Element Procedures", 2nd Edition (.pdf) Solutions to exercises in the book "Finite Element Procedures", 2nd Edition, 2014 are given in this manual (.pdf) The Chinese translation of the 2nd edition is also available: Vol. 1 Vol. 2
These manuals describe in short form the theory used in ADINA Structures, Thermal, CFD and EM, and give hints for modeling problems correctly. For ADINA users: manuals
Bathe, KlausJürgen; Baig, M. M. I. Source: Computers & Structures, v 83, 2513 – 2534, 2005. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: Transient analysis of nonlinear problems in structural and solid mechanics is mainly carried out using direct time integration of the equations of motion. For reliable solutions, a stable and efficient integration algorithm is desirable. Methods that are unconditionally stable in linear analyses appear to be a natural choice for use in nonlinear analyses, but unfortunately may not remain stable for a given time step size in large deformation and long time range response solutions. A composite time integration scheme is proposed and tested in some example solutions against the trapezoidal rule and the Wilson thetamethod, and found to be effective where the trapezoidal rule fails to produce a stable solution. These example results are indicative of the merits of the composite scheme. Keywords: finite element method, composite integration, trapezoidal rule
Kohno, Haruhiko; Bathe, KlausJürgen. Source: Int. J. Num. Meth. in Fluids, v 51, 673699, 2006. ISSN: 02712091 (print); 10970363 (online) Publisher: John Wiley & Sons, Ltd. Abstract: A flowconditionbased interpolation finite element scheme is presented for use of triangular grids in the solution of the incompressible NavierStokes equations. The method provides spatially isotropic discretizations for low and high Reynolds number flows. Various example solutions are given to illustrate the capabilities of the procedure. Keywords: incompressible flows, stability, accuracy, flowconditionbased interpolation
Goaloriented Error Estimation in the Analysis of Fluid Flows with Structural Interactions Grätsch, Thomas; Bathe, KlausJürgen. Source: Comp. Meth. in Applied Mech. and Eng., v 195, 56735684, 2006. ISSN: 00457825 Publisher: Elsevier Ltd Abstract: We present some developments for the extension of goaloriented error estimation procedures to the analysis of Navier–Stokes incompressible fluid flows with structural interactions. Particular focus is given on error assessment of specific quantities of interest defined on the structural part. The goal is to establish relatively coarse meshes to model the fluid flow but achieve acceptable accuracy in the quantities of interest. A nonlinear goaloriented error estimation procedure is presented which is applicable to general nonlinear analyses. Some illustrative solutions using ADINA are given. Keywords: goaloriented error estimation, Navier–Stokes fluid flow, nonlinear structures, interactions; FSI
Lee, PhillSeung; Bathe, KlausJürgen. Source: Computers & Structures, v 83, 6990, 2005. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: The objective of this paper is to gain insight into finite element discretizations of shells using the basic shell mathematical model and, in particular, regarding the sources of "locking". We briefly review the "basic shell mathematical model" and present a formulation of shell finite elements based on this model. These shell finite elements are equivalent to the widelyused continuum mechanics based shell finite elements. We consider a free hyperboloid shell problem, which is known to be difficult to solve accurately. Using a fine mesh of MITC9 elements based on the basic shell mathematical model, a detailed analysis is performed giving the distributions of all strain terms. A similar analysis using the MITC6 shell element shows why this element locks when the shell thickness is very small. Keywords: shell structures, basic shell mathematical model, MITC shell elements
Grätsch, Thomas; Bathe, KlausJürgen. Source: Int. J. for Numerical Methods in Eng., v 63, 709736, 2005. ISSN: 00295981 CODEN: IJNMBH Publisher: John Wiley & Sons, Ltd Abstract: In this paper, we first present a consistent procedure to establish influence functions for the finite element analysis of shell structures, where the influence function can be for any linear quantity of engineering interest. We then design some goaloriented error measures that take into account the cancellation effect of errors over the domain to overcome the issue of overestimation. These error measures include the error due to the approximation in the geometry of the shell structure. In the calculation of the influence functions we also consider the asymptotic behaviour of shells as the thickness approaches zero. Although our procedures are general and can be applied to any shell formulation, we focus on MITC finite element shell discretizations. In our numerical results, influence functions are shown for some shell test problems, and the proposed goaloriented error estimation procedure shows good effectivity indices. Keywords: shell structures, influence functions, goaloriented error estimation, MITC shell elements
Grätsch, Thomas; Bathe, KlausJürgen. Source: Computers & Structures, v 83, 235265, 2005 ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: In this paper we review the basic concepts to obtain a posteriori error estimates for the finite element solution of an elliptic linear model problem. We give the basic ideas to establish global error estimates for the energy norm as well as goaloriented error estimates. While we show how these error estimation techniques are employed for our simple model problem, the emphasis of the paper is on assessing whether these procedures are ready for use in practical linear finite element analysis. We conclude that the actually practical error estimation techniques do not provide mathematically proven bounds on the error and need to be used with care. The more accurate estimation procedures also do not provide proven bounds that, in general, can be computed efficiently. We also briefly comment upon the state of error estimations in nonlinear and transient analyses and when mixed methods are used. Keywords: finite element analysis, a posteriori error estimation, goaloriented error estimation, dual problem, practical procedures
Kohno, Haruhiko; Bathe, KlausJürgen. Source: Int. J. for Numerical Methods in Eng., v 63, 197217, 2005. ISSN: 00295981 CODEN: IJNMBH Publisher: John Wiley & Sons, Ltd Abstract: The flowconditionbased interpolation (FCBl) finite element approach is Studied in the solution of advectiondiffusion problems. Two FCBI procedures are developed and tested with the original FCBI method: in the first scheme, a general solution of the advectiondiffusion equation is embedded into the interpolation, and in the second scheme, the linkcutting bubbles approach is used in the interpolation. In both procedures, as in the original FCBI method, no artificial parameters are included to reach stability for high Peclet number flows. The procedures have been implemented for twodimensional analysis and the results of some test problems are presented. These results indicate good stability and accuracy characteristics and the potential of the FCBI Solution approach. Keywords: advectiondiffusion, stabilization, flowconditionbased interpolations
Elabbasi, Nagi; Hong, JungWuk; Bathe, KlausJürgen. Source: Int. J. of Mechanics and Materials in Design, v 1, 316, 2004. ISSN: 15691713 (Print) 15738841 (Online) Publisher: Springer Netherlands Abstract: In this paper we examine briefly the reliability of solution needed for the accurate and effective analysis of engineering design problems involving contact conditions. A general finite element formulation for treating the frictional contact problem using constraint functions is first summarized. Then we address general reliability issues and those related to the selection of appropriate elements that provide optimal performance. These elements of course do not lock and would provide the best solution an analyst can expect when simulating a design problem. Reliability issues specific to the contact formulation are also presented. A promising procedure to increase the reliability of an analysis is the method of finite spheres. The method does not require a mesh and in particular can be used with a finite element discretization as described in the paper. Finally, the results of several illustrative analysis problems are given. Keywords: contact, reliability, finite element solution, finite spheres, design
Hong, JungWuk; Bathe, KlausJürgen. Source: Computers & Structures, v 83, 13861395, 2005. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: We present a technique to couple finite element and finite sphere discretizations. The finite elements and finite spheres are coupled with full displacement compatibility. We also present a technique in which a finite element discretization is enriched with finite spheres. We consider twodimensional conditions and present solutions to illustrate the analysis procedures. Keywords: finite element, finite sphere, discretization, coupling
Lee,PhillSeung; Bathe, KlausJürgen. Source: Computers & Structures, v 82, 945962, 2004. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: We present a simple methodology to design isotropic triangular shell finite elements based on the Mixed Interpolation of Tensorial Components (MITC) approach. Several mixedinterpolated isotropic triangular shell finite elements are proposed. We perform wellestablished numerical tests and show the performance of the new elements. Keywords: shell structures, finite elements, triangular elements, MITC shell elements
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