Optimal design of trusses by approximate compatibility

Abstract

Optimal design of elastic trusses is formulated as an approximate linear programming problem. Using the force method of analysis, the redundant forces are expressed in linearized terms of the design variables. The solution of the resulting linear programming problem can be viewed as an exact optimum for a truss with different displacements corresponding to the unknown redundants. The latter displacements, computed directly from the linear programming solution, indicate the degree of not satisfying the compatibility conditions. This information can be used to introduce imaginary displacements in subsequent iteration cycles. An iterative procedure of solution is proposed in which both the design and the imaginary displacements are modified until the compatible optimal solution is reached. Each iteration cycle requires the solution of a linear programming problem. The proposed procedure provides more flexibility in the solution process than the usual algorithms based on a sequence of linear programs and may improve the convergence. Numerical examples illustrate the application of this procedure in optimal design of simple trusses.