Elastic Analysis with Indeterminate Boundary Conditions

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Abstract
Elastic analysis of structures with boundary conditions where each may assume either of two configurations is considered. A trial and error approach is shown to be unreliable. It is proved that the principles of minimum potential energy and minimum complementary potential can be generalized to account for this type of boundary condition. These generalizations are used to formulate the analysis as a nonlinear programming problem in general, and as a quadratic programming problem for a linear material. Numerical examples of simple structures illustrate this approach.

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