Generalized Variational Principles for Solutions of Statically Indeterminate Trusses under Mechanical-Thermal-Assembly Loadings

Abstract

This paper presents an extension of an energy-based method for analysis of statically indeterminate trusses under mechanical-thermal-assembly loadings. Using the Lagrange multiplier method, internal forces of statically indeterminate trusses under the effect of mechanical-thermal-assembly loadings are investigated by generalized variational principles. Introducing the Lagrange multipliers and connecting with static equilibrium equations, a new functional from unconditional generalized variational principles is presented. By solving the extremal problem of the new functional, a matrix form of general solutions for internal forces of statically indeterminate trusses is obtained. Compared with the literature results, the accuracy and universality of the present method is confirmed. The results show that it cannot only overcome the defect of compatibility equations by traditional geometry method, but that it also has the advantages of simple process and good generality.