Group theoretical formulation of nonsymmetrical systems by the group supermatrix procedure

Abstract

The group supermatrix procedure, developed by Zlokovic for systems with symmetry properties described by groups, can be also applied to systems without symmetry. Transformation of a nonsymmetrical system into a system with symmetry properties is accomplished by symmetrization of support conditions, by adding fictitious structural parts and by removing existing ones. The generalized displacements and forces in the above symmetrized system coincide with corresponding values in the nonsymmetrical system. The Group supermatrix procedure performs the analysis for each G-invariant subspace separately, using only a part of the structure. This provides, in comparison with conventional methods, a drastic reduction in the amount of data input, computation and necessary memory space of the computer.