The Loop Resultant Method For Static Structural Analysis

This work deals with the loop resultant method applied to linear static response of statically indeterminate rod-systems. The method uses the representation of this system in the form of a union of statically indeterminate loops. An algorithm for construction the flexibility matrix of the system is proposed. The unknowns of a system are the loop resultants. This method is based on the use of compatibility equations of deformations, the general solution of homogeneous equations of equilibrium is obtained by transposition of the compatibility matrix. The advantages of this method are the number and location of zero blocks and non-zero blocks of the system flexibility matrix depend only on the numbering of loops. Application of this method is considered for analysis of structural frame.