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
Montáns, Francisco Javier; Bathe, KlausJürgen. Source: Int. J. for Numerical Methods in Eng., v 63, 159196, 2005. ISSN: 00295981 CODEN: IJNMBH Publisher: John Wiley & Sons, Ltd. Abstract: In this paper an algorithm for large strain elastoplasticity with isotropic hyperelasticity based on the Multiplicative decomposition is formulated. The algorithm includes a (possible) constitutive equation for the plastic spin and mixed hardening in which the principal stress and principal backstress directions are not necessarily preserved. It is shown that if the principal trial stress directions are preserved during the plastic flow (as assumed in some algorithms) a plastic spin is inadvertently introduced for the kinematic/mixed hardening case. If the formulation is performed in the principal stress space, a rotation of the backstress is inadvertently introduced as well. The consistent linearization of the algorithm is also addressed in detail. Keywords: large strains, computational plasticity, plastic spin, kinematic hardening, cyclic plasticity, logarithmic strains
Chapelle, Dominique; Ferent, A.; Bathe, KlausJürgen. Source: Mathematical Models & Methods in Applied Sciences, v 14, 105142, 2004. ISSN: 02182025 Publisher: World Scientific Publishing Company Abstract: We focus on a family of shell elements which are a direct generalization of the shell elements most commonly used in engineering practice. The elements in the family include the effects of the throughthethickness normal stress and can be employed to couple directly with surrounding media on either surfaces of the shell. We establish the "underlying" mathematical model of the shell discretization scheme, and we show that this mathematical model features the same asymptotic behaviors  when the shell thickness becomes increasingly smaller  as classical shell models. The question of "locking" of the finite element discretization is also briefly addressed and we point out that, for an effective finite element scheme, the MITC approach of interpolation is available. Keywords: shells, general shell elements, asymptotic behaviors, locking
Bathe, KlausJürgen; Montáns, Francisco Javier. Source: Computers & Structures, v 82, 535539, 2004. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: We address herein the calculation of Prager’s hardening parameter in computational plasticity when mixed hardening is considered. We consider two approaches to evaluate the mixed hardening response; namely, based on splitting the plastic strains and based on splitting the plastic modulus. For a onedimensional stress–strain curve with nonlinear hardening, the proper calculation of Prager’s hardening parameter is demonstrated and some comparisons and insight are provided. Keywords: Computational plasticity, cyclic response, Prager’s rule, Mixed hardening
Bathe, KlausJürgen; Zhang, Hou. Source: Int. J. for Numerical Methods in Eng., v 60, 213232, 2004. ISSN: 00295981 CODEN: IJNMBH Publisher: John Wiley & Sons, Ltd. Abstract: The objective in this paper is to present some developments for the analysis of NavierStokes incompressible and compressible fluid flows with structural interactions. The incompressible fluid is discretized with a new solution approach, a flowconditionbased interpolation finite element scheme. The highspeed compressible fluids are solved using standard finite volume methods. The fluids are fully coupled to general structures that can undergo highly nonlinear response due to large deformations, inelasticity, contact and temperature. Particular focus is given on the scheme used to couple the fluid media with the structures. The fluids can also be modelled as lowspeed compressible or slightly compressible media, which are important models in engineering practice. Some solutions obtained using ADINA are presented to indicate the analyses that can be performed. Keywords: fluid flow, incompressible, compressible, FSI, ADINA
De, Suvranu; Hong, JungWuk; Bathe, KlausJürgen. Source: Computational Mechanics, v 31, 2737, 2003 ISSN: 01787675 (Print) 14320924 (Online) Publisher: Springer Abstract: In this paper we report some recent advances regarding applications using the method of finite spheres; a truly meshfree numerical technique developed for the solution of boundary value problems on geometrically complex domains. First, we present the development of a preprocessor for the generation of nodal points on twodimensional computational domains. Then, the development of a specialized version of the method of finite spheres using point collocation and moving least squares approximation functions and singular weight functions is reported for rapid computations in virtual environments involving multisensory (visual and touch) interactions. Keywords: method of finite spheres, meshfree method, ADINA, surgical simulation
Towards Improving the MITC9 Shell Element Bathe, KlausJürgen; Lee, PhillSeung; Hiller, JeanFrançois; Source: Computers & Structures, v 81, 477489, 2003. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: Our objective in this paper is to present some results regarding the predictive capabilities of the MITC9 shell element when the tying points in the element are changed. The MITC9 element is a general ninenode shell element based on the formulation approach of using mixedinterpolated tensorial components. Different tying points are very simple to implement and are not decreasing the computational efficiency of the element. Hence, the use of the “best” tying points is clearly of value. Keywords: MITC9 shell element, mixedinterpolated tensorial components, tying points
Hiller,JeanFrançois; Bathe, KlausJürgen. Source: Computers & Structures, v 81, 639654, 2003. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: We consider the problem of assessing the convergence of mixedformulated finite elements. When displacementbased formulations are considered, convergence measures of finite element solutions to the exact solution of the mathematical problem are well known. However when mixed formulations are considered, there is no wellestablished method to measure the convergence of the finite element solution. We first review a number of approaches that have been employed and discuss their limitations. After having stated the properties that an ideal error measure would possess, we introduce a new physicsbased procedure. The new proposed error measure can be used for many different types of mixed formulations and physical problems. We illustrate its use in an assessment of the performance of the MITC family of shell elements. Keywords: mixedformulated finite elements, error measure, MITC shell elements
Bathe, KlausJürgen; Chapelle, Dominique; Lee, PhillSeung. Source: Int. J. for Numerical Methods in Eng., v 57, 10391052, 2003. ISSN: 00295981 CODEN: IJNMBH Publisher: John Wiley & Sons, Ltd Abstract: In general, shell structural problems can be identified to fall into one of the categories of membranedominated, bendingdominated and mixed shell problems. The asymptotic behaviour with a welldefined loadscaling factor shows distinctly into which category a given shell problem falls. The objective of this paper is to present a shell problem and its solution for which there is no convergence to a welldefined loadscaling factor as the thickness of the shell decreases. Such shells are unduly sensitive in their behaviour because the ratio of membrane to bending energy stored changes significantly and indeed can fluctuate with changes in shell thickness. We briefly review the different asymptotic behaviours that shell problems can display, and then present the specific problem considered and its numerical solution Using finite element analysis. Keywords: shells, asymptotic analysis, finite element solution
Lee,PhillSeung; Bathe, KlausJürgen. Source: Computers & Structures, v 80, 235255, 2002. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: The objective of this paper is to demonstrate how the asymptotic behavior of a shell structure, as the thickness (t) approaches zero, can be evaluated numerically. We consider three representative shell structural problems; the original Scordelis–Lo roof shell problem, a herein proposed modified Scordelis–Lo roof shell problem and the partly clamped hyperbolic paraboloid shell problem. The asymptotic behavior gives important insight into the shell load bearing capacity. The behavior should also be known when a shell problem is used to test a shell finite element procedure. We briefly review the fundamental theory of the asymptotic behavior of shells, develop our numerical schemes and perform the numerical experiments with the MITC4 shell finite element. Keywords: shells, asymptotic behaviors, Ffnite element solutions
Bathe, KlausJürgen; Zhang, Hou. Source: Computers & Structures, v 80, 12671277, 2002. ISSN: 00457949 CODEN: CMSTCJ Publisher: Elsevier Ltd Abstract: The objective of this paper is to demonstrate how the asymptotic behavior of a shell structure, as the thickness (t) approaches zero, can be evaluated numerically. We consider three representative shell structural problems; the original Scordelis–Lo roof shell problem, a herein proposed modified Scordelis–Lo roof shell problem and the partly clamped hyperbolic paraboloid shell problem. The asymptotic behavior gives important insight into the shell load bearing capacity. The behavior should also be known when a shell problem is used to test a shell finite element procedure. We briefly review the fundamental theory of the asymptotic behavior of shells, develop our numerical schemes and perform the numerical experiments with the MITC4 shell finite element. Keywords: shells, asymptotic behaviors, finite element solutions
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