Abstract
Instead of a priori assumed shape functions a numerical solution of all field equations can be used to compute the finite element matrices. Finite difference scheme with a midpoint is used to integrate the canonic set of ordinary differential equations. The equations describe the 2-point boundary value problem for uni-dimentional structural problems. The matrices of such exact finite elements are obtained as a result of solution of the appropriate set of linear algebraic equations. An algorithm for the analysis of a modified eigenproblem is presented. Numerical examples deal with simple bar structures for which analytical solutions exist. In addition to [13] a new example deals with buckling of cooling tower models under combined loads and a comparsion of results with those obtained experimentally is made. Canonic set of incremental equations is given in Appendix for a circular, slightly curved bar.
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