Optimization of multi-element models of structures with integral constraints on unsteady responses

Abstract

Object and purpose of research. The study focuses on management of dynamic parameters of structures, the load on which has unsteady character in accordance with a given frequency spectrum. Based on the earlier obtained [8, 15] matrix relations of sensitivity analysis, effective design iteration algorithms, which satisfy Kuhn–Tucker optimum conditions, are developed and implemented in software. Subject matter and methods. The methods used are a displacement method version of the beam finite-element technique, analytical and semi-analytical methods of taking a derivative with respect to frequencies, shapes as well as unsteady displacements of structure integrally averaged in space and time, methods of simple iterations with relaxation smoothening, methods of linearization of recurrent relations of optimality conditions and reduction of conditional minimization problem to unconditional problem using Lagrange factors. Main results. For FE beam model with a large number of finite elements, minimization mass problems are solved at restricted integral norm of deflection for various unsteady excitation at a given time interval. Comparison of optimization procedures are made for accuracy and efficiency using direct implicit differentiation of difference scheme and normal mode method for response. Conclusion. Similar results are obtained by different methods of calculating the unsteady response and performance of sensitivity analysis. Efficient management of the mass and stiffness distribution is demonstrated with a relatively high gain in isoperimetric formulation.

Keywords

• indirect optimization methods
• sensitivity analysis
• beam finite elements
• derivatives of unsteady displacements
• method of normal coordinates
• newmark beta-method
• integral constraints
• lagrange factors