Loading optimization of the metal trusses has a variational basis. The universal criterion of optimization is the minimum of potential energy of the system (additional energy) in functional space expanded at the expense of functions fields of configuration and (or) material modules, and load. Under the condition of homogeneous linear elastic material optimal truss represents as quasiuniresistant virtual system with internal forces Ni/ⱷi (ⱷi – decrease coefficient of designed metal resistance of to tension and compression. The value ∑Nili (l is pivot length) is in general case the characteristic of the degree of a priori stability of truss, in special case (the load at the line, connecting supports) determines optimal variant of loading. As numerical experiment was consider the distribution of load ∑Fi=const for the truss with descending (ascending) pivot. It is established the independence of optimal loading variant from truss grating structure.

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.

Yuriev A.G., Zinkova V.A., Smolyago N.A., Yakovlev O.A. STRUCTURE OPTIMIZATION OF THE METAL TRUSSES Efficient method structure determination of metal truss has variational basis. Variational statement of problem is a fundamental approach of intention realization. From it follows universal criterion of optimization, connecting with minimum of potential energy of the system in function space expanded at the expense of function fields of configuration and (or) material moduls. Under the condition of homogeneous linear elastic material optimal truss represents as uniresistant virtual system with internal forces N/ i ( i decrease coefficient of designed resistance of material). As numerical example was considered the determination of optimal structure of the truss with the consoles. Of the four variants, the minimum amount of material obtained for the truss with downward diagonals and the horizontal fragment of the upper belt. At the stage of optimal geometry determination of a truss at a given geometry the problem is solved strictly by variational methods of structural synthesis, and at stage of the topology optimization by comparison of admissible variants. However, in both cases is present a single criterion of optimality, carrying into minimum of material expense.

Loading optimization of the metal trusses has a variational basis. The universal criterion of optimization is the minimum of potential energy of the system (additional energy) in functional space expanded at the expense of functions fields of configuration and (or) material modules, as well load. The proposed variational method of truss synthesis is based on the principle of possible work and generalization of the variational principles of Lagrange and Castigliano by expanding the functional space of geometric parameters. The criterion of equal strength of the truss established in the linear statement of the variational problem creates the prerequisites for finding its optimal topology and geometry when specifying the type of load, directive parameters, mechanical characteristics of the material, and the flexibility of compressed rods. The global minimum potential energy of deformation of the optimal truss corresponds to the global minimum material consumption. As numerical experiment was consider the distribution of load P F i = const for the truss with descending (ascending) pivot. It is established the independence of optimal loading variant from truss grating structure.

Attempts to engage this issue on the basis of the criterion of minimum volume (mass) of the material were unsuccessful because of the difficulty of finding a global minimum. T. The optimal solution of the design of the truss in respect of its topology, geometry, areas and shapes of cross sections is based on variational principles for structural synthesis. Stemming from their universal optimality criterion leads to a minimum consumption of material. The specificity of the compressed rods is reflected in the expression of the strain energy. At the same time a complete solution of compressed rods is carried out by additional research on the state of the unconstrained or constrained buckling.