The theorems of structural variation for rectangular finite elements for plate flexure

The theorems of structural variation predict the forces and displacements throughout a structure without the need of fresh analysis when the physical properties of one or more members are altered or even its topology is changed due to removal of one or more of its elements. It has been shown that a single linear elastic analysis of a parent structure under the applied loads and a set of unit-loading cases is sufficient to determine the elastic, non-linear elastic and even elastic–plastic response of number of related frames. These theorems later are extended to triangular, quadrilateral and solid cubic finite element structures. In this paper, the theorems of structural variation are extended to cover the rectangular finite elements for plate flexure. The unit-loading cases required to study the modification of a single element are derived. The displacements and nodal forces obtained from these unit-loading cases are used to calculate the variation factors. Multiplication of the response of the parent structure by these variation factors simply yields the response of the new structures where one or more of its members are altered or totally removed. Two examples are included to demonstrate the application of these theorems.