R.V. Nambiar

Closed-form stiffness matrices for the linear strain and quadratic strain tetrahedron finite elements

Abstract In this paper the development of closed-form representations of element stiffness matrices and the equivalent nodal loads for the linear strain and quadratic strain straight edge tetrahedral elements are presented. The closed-form representation of the element stiffness matrix and the equivalent nodal loads were performed using symbolic algebra. Dramatic time savings result in the element stiffness matrix evaluation phase of the FEM process when the closed-form representation is used as compared with the use of Gaussian quadrature.

Closed-form expressions for the linear and quadratic strain tetrahedral finite elements

Abstract The use of closed-form expressions in a finite element code significantly reduces the time required to evaluate the element stiffness matrix as compared to Gaussian quadrature. The development of closed-form expressions for the element stiffness matrices for the plane-faced linear strain and quadratic strain tetrahedral finite elements has been previously presented elsewhere. In this paper, a reformulation of the process is given which significantly reduces the size of the element stiffness expressions. Expression growth is prevented by decomposing the strain-displacement matrix and utilizing a new matrix which is geometry and material dependent.

A study of adaptively remeshed finite element problems using higher order tetrahedra

Abstract A study has been performed for various three-dimensional elasticity problems to evaluate the performance of a three-dimensional FEM preprocessor, processor and companion remeshing modules. Both straight-sided and curve-sided tetrahedral finite elements were employed. All the problems analyzed started with initial meshes varying from 5 to 20 linear strain or quadratic strain tetrahedral elements. Remeshing was based on Zienkiewicz-Zhu error indicators obtained from the processor. The modules were used iteratively for each problem until the estimated error converged to a user specified value. Comparisons based on accuracy, convergence and computational efficiency were performed for all problems and element combinations.

Closed-form error estimators for the linear strain and quadratic strain tetrahedron finite elements

Abstract Closed-form representations of the Zienkiewicz-Zhu error estimators for straight edge linear and quadratic strain tetrahedral elements are presented. The closed-form representation of the element error estimators was developed using symbolic algebra. Dramatic computational time savings result in the element error estimator evaluation phase of the FEM process when the closed-form representation is used as compared with the use of Gaussian cubature.

Shape design sensitivity analysis using closed-form stiffness matrix for hierarchic triangular elements

Abstract Shape design sensitivity analysis for finite element analysis using straight-sided hierarchic triangular elements is considered in this paper. Using a recently developed closed-form stiffness matrix, the sensitivity analysis is carried out by direct differentiation of the system equations for finite element analysis. That is, the term ∂K / ∂α required in sensitivity analysis is formulated in the closed form. This is in contrast with prior formulations which utilize finite differences (the semianalytical formulation) and numerical integration to obtain these terms. Both the displacement sensitivity analysis and the strain and stress sensitivity analysis are addressed in this paper.

Explicit expressions for element coordinate transformations by symbolic manipulation

Abstract A symbolic manipulator has been used to develop explicit expressions for element stiffness matrices in global coordinates. Numerical experiments using these expressions give execution time reductions of as much as four to one or more, when compared with efficient matrix multiplication methods to achieve the same result. A three dimensional beam element and a general element are treated.

C routines for fem applications

Abstract C routines for in-core assembly and direct solution of the equations which arise in linear finite element applications are presented. The skyline storage mode is employed, and results of timing experiments with and without the use of pointer incrementation are presented.

A description of an expert system for finite element modeling and analysis

Abstract Finite element analysis is an integral part of the structural analysis process in the design and development of parts and assemblies. Various levels of integration exist between design systems and finite element modeling systems. The feasibility of a knowledge-based system to tightly couple product design systems and finite element analysis systems was investigated. A framework incorporating feature-based design systems, heuristics-based planning modules and procedural pre-processing/solving/adaptive refinement schemes was developed. The pertinent modules of the framework were organized into a prototype and implemented in the VAX environment utilizing the EUCLID geometric modeling system, CLIPS expert system development tools, PATRAN 2.3 finite element pre-processing system, a finite element solver and an adaptive refinement system developed specially for the framework. The scope of the research work was limited to static stress analysis. The results of the research indicated that design systems can be successfully integrated with finite element analysis systems in a knowledge-based framework. The framework was also found to be suitable for finite element-based structural optimization and self-learning processes.