Developments in Discrete Element Finite Deflection Structural Analysis by Function Minimization

摘要

The discrete element energy search method of structural analysis is extended to predicting the geometrically nonlinear behavior of plate and shell type structures. Numerical results for example problems exhibiting nonlinear bending-membrane coupling and stable post-buckling behavior are presented. The results of a laboratory type experimental program, designed to provide data for comparison with analytical behavior predictions, are reported. It is shown that displacement patterns formed from products of one-dimensional interpolation functions can be used to generate a useful class of shell discrete elements, including geometric nonlinearity. These conforming elements can be joined together at arbitrary angles, although the current computer program is limited to tangential and right angle joining. While the major portion of this research program was based upon the principle of minimum potential energy, a rectangular plate discrete element exhibiting bending membrane coupling is developed within the Reissner energy framework. Energy search methods of structural analysis based on potential energy formulations and gradient minimization algorithms are found to be computationally competitive with conventional solution procedures. (Author)