Truss Design Calculation

Abstract

the completeness of the truss design calculation is its configuration and dimensions when specifying the type of loading, material characteristics and directive dimensions. The problem of equilibrium stability with an unknown location of compressed rods hindered the optimization of the topology and geometry of the truss. The proposed variational method of truss synthesis is based on the principle of possible operation and generalization of the variational principles of Lagrange and Castigliano by expanding the functional space of geometric parameters. The solution of a physically linear isoperimetric problem for a given volume of the truss material allowed to establish its quasi-equal stress, which became the design criterion for the formulation of the geometry optimization problem. Its condition is the stationarity of the functional with respect to variable geometric parameters for a given flexibility of compressed rods. The iterative procedure, caused by a change in the initially accepted signs of longitudinal forces, is based both on their direct adjustment and on the change in the flexibility of individual rods. The global minimum of potential strain energy of the optimal truss is accompanied by a global minimum of material consumption. The proposed software allows to conduct automated design calculation of the truss. An example of designing a mechanical truss is considered.