Structural Analysis of Solids

Abstract

No new pitfalls are revealed in this use of the stiffness method for analyzing three-dimensional solids. Numerical experiments show the importance of using the monotonic convergence criteria. They demonstrate the desirability of using energy relations to define loading. They verify the superior accuracy of the prism geometry over the tetrahedron. The relative accuracy of various matrices correlates well with the relative values of the stiffness matrix trace and latent roots. The bases for development of four stiffness matrices are presented and coefficients cited for the matrices of special interest. Six loadings on a rectangular prism are analyzed. Exact solutions are compared with numerical results for one, eight, and sixty-four subprisms. All subprisms have the same shape. Using this shape, the trace and latent roots of each matrix are obtained. It is shown that the smaller the trace and roots, the more accurate the matrix is in solving problems.