Abstract
A unifying structure of semi-infinite programming has been the linear space of generalized finite sequences. While providing a duality theory, their use also opens up promising avenues for numerical treatment. In this paper the unification is extended to some problems in continuum physics whose mathematical formulations involve choices of function spaces, techniques of integration by parts in one and two dimensions, and finite element numerical approximations. The extension produces a biextremal formulation of equilibrium problems in continuum mechanics having material stress and displacement variables which is equivalent to a dual pair of infinite linear programs. Analogous to two-person game theory each problem has its own set of variables (stresses or displacements but not both) augmented by the dual variables associated with some of the constraining inequalities of the companion problem. Simultaneously, generalized finite sequences generate a class of generalized finite elements, including for example, the space of all 4-node nonlinear quadrilateral elements.
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Kortanek, K.O. (1985). Semi-Infinite Programming and Continuum Physics. In: Anderson, E.J., Philpott, A.B. (eds) Infinite Programming. Lecture Notes in Economics and Mathematical Systems, vol 259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46564-2_6
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DOI: https://doi.org/10.1007/978-3-642-46564-2_6
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