Characteristics Of Several Functions And Research Of Optimization Algorithms For Trusses Including Self-Weight Loads

Characteristics of some functions and their sensitivities of trusses with self-weight loads are little researched. At lack of them, the convergence of structrural optimization algorithm could not effectively guaranteed. The truss optimization at the same time with stress, displacement and frequency constraints is not yet mature. Its optimal solution is difficult to be obtained.For topology, sizing, geometry and their simultaneous optimization of trusses with self-weight loads, the new algorithms of truss optimization are developed, based on studying the characteristics of certain truss functions and their sensitivities, and the extremum necessary conditions of constraint optimization problem. Then, the algorithm implementation and numerical examples are discussed.(1) The characteristics of nodal displacements, axial stresses, axial strain energy and natural frequencies and their sensitivities of trusses with self-weight loads are discussed, according to the rules of cross-sectional areas and nodal coordinates changing as the same proportion, respectively. Then, the characteristics of the maximum bending stress of uniform section bar, and methods for controlling the maximum bending stress and preventing buckling of compressive bar are discussed, on the basis of the theory of the beam with lateral uniform load.(2) On the basis of the analysis of the KKT conditions, and the extremum necessary conditions of dual objective function, the optimization direction and optimal step length factor of the KKT multipliers are discussed to directly solve the multiplier with boundary information of single state constraint, or to iteratively solve the multipliers of multi state constraints.However, according to the derived characteristics of the function sensitivities of trusses with self-weight loads, the built-up principle and its convergence condition of the parabola method for direct iteration and optimization iteration, as well as its step length factor automatically determined are discussed.(3) For the weight minimization under axial strain energy constraint used to the topology optimization of trusses with self-weight loads, the application of the optimization theory for single state constraint is discussed, in combination with the characteristics of the axial strain energy function derived in this paper. Namely:on the basis of its KKT conditions and the principle of dual programming, the establishment and application of work-weight distribution criteria, the solution formula of radial scaling factor and how to obtain non-negative multiplier including constraint boundary information, the establishment of the parabola method for direct iteration and its characteristics, and program realization and numerical examples, etc., are discussed.(4) For the automatical optimization of the size and topology of trusses with self-weight loads, the application of the optimization theory for multi state constraints is discussed, in combination with the characteristics of nodal displacements and axial stresses and natural frequencies derived in this paper. Namely:on the basis of its KKT conditions and the principle of dual programming, the iteration solution of the multipliers and automatic determination of its optimal step length factor, the parabola method for the optimization iteration of cross-sectional areas and automatic determination of its step length factor, and program realization and numerical examples, etc., are discussed.(5) For the automatical optimization of the size, geometry and topology of trusses with self-weight loads, the application of the optimization theory for multi state constraints is discussed, in combination with the characteristics of nodal displacements and axial stresses and natural frequencies derived in this paper. Namely:on the basis of its KKT conditions and the principle of dual programming, the iteration solution of the multipliers and automatic determination of its optimal step length factor, the parabola method for the optimization iteration of nodal coordinates and automatic determination of its step length factor, and program realization and numerical examples, etc., are discussed.Above points are verified by the numerical examples of the topology, size and geometry optimization of certain plane and space trusses with self-weight loads. The optimization processes are automatic and higher efficient. The optimization results are good.