Analysis and behavior of grid structures

Symbolic computation in structural engineering

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

Closed form expressions for the stiffness matrix and a simple error estimator and error indicator are derived for plane straight sided triangular finite elements in elasticity problems. The calculation of the error estimator is performed on an element by element basis, and is found to be very accurate and efficient. In general, the solutions for benchmark problems using the error indicators for selective refinement of the regions show accelerated convergence when compared to the convergence rate of solutions using uniform mesh refinement. Evaluation of the stiffness matrices and error estimators using explicit formulations is found to be several times faster than numerical integration.

Closed form stiffness matrices and error estimators for plane hierarchic triangular elements

Closed-form stiffness matrices for higher order tetrahedral finite elements

Convenient generation of stiffness matrices for the family of plane triangular elements

An algorithm to generate universal matrices for plane triangular finite elements for the general ‘quasi-harmonic’ equation is presented. For every member of the triangle family three numerical universal matrices are obtained which are independent of the size, shape and ‘material’ properties of the element. Of these, two are basic and the third can be generated from one of these two. The element ‘stiffness’ matrix is conveniently generated by manipulating these two basic matrices taking into account the size, shape and material properties of the element in a simple manner.

C.Jeyachandra Bose

Papers

Convenient generation of stiffness matrices for the family of plane triangular elements

A note on universal matrices for triangular finite elements for the quasi-harmonic equation

On stiffness matrices for C0 continuous tetrahedra