Stiffness Matrices of Symmetric Structures

By considering the physical symmetry of a structure, a number of pairs of the elements in the upper (or lower) triangular part of the stiffness matrix are equal in absolute value. Such relationships are described in terms of degrees of freedom in ``intrinsic coordinates.'' For similar nodes on each side of a plane of symmetry, the intrinsic coordinates of the nodes are mirror images of each other. The stiffness coefficients for corresponding degrees of freedom in the intrinsic coordinates for similar nodes are equal. The number of independent and dependent coefficients are delineated. For one fold symmetry, the number of independent stiffness coefficients is (n+2)n/4, and for two and three fold symmetry, it is (n+4)n/8 and (n+8)n/16, respectively. The relation of the signs of the dependent and independent coefficients is developed. The information may be used to save computation efforts needed for the formulation of stiffness matrices of symmetric structures.