A matrix theory of elastic-locking structures

Abstract

The theory developed exhibits the following peculiar features: structures are discretizised in finite elements, the constitutive laws piecewise linearized, the problem is split in a preliminary linear elastic solution and a “corrective” nonlinear subproblem; concepts and techniques of quadratic and linear programming theory are utilized. The main results are: for the analysis under given loads and dislocations, a pair of extremum theorems for locking stresses, corresponding to dual quadratic programs; for the limit analysis with respect to locking situations two already known theorems, which are here deduced from the solvability conditions of the above quadratic programs and formulated as dual linear programs. The extension of the results to imperfectly locking behavior is carried out. Some examples illustrate the solution techniques based on the theory expounded.