Research On Reliability-based Topology Optimization Of Continuum Structure

Structure optimization and reliability design are irreplaceable roles in modern industrial design and mechanical design field. Structure optimization, generally, divided into size optimization, shape optimization and topology optimization. Topology optimization design is always the hot spot in structure optimization domain. Topology optimization design can make the industrial design personnel get the structure optimal topological shape through the operation method and the computer program in the design stage, so as to provide a powerful guidance for structure design. Continuum structure topology optimization is an important branch of topology optimization. Generally, continuum structure topology Optimization is based on deterministic parameters, In fact, the parameters of material composed and the loads applied etc. are random parameters. These random parameters lead to the optimization results get by deterministic not adapt to the requirement of engineering, the reliability of structure is not ensure. Obviously, the reliability based topology optimization is more necessary; has important theoretical significance and engineering practical value.This dissertation take the Program of Changjiang Scholars and Innovative Research Team in University(No. IRT0816), Key National Science&Technology Special Project on "High-Grade CNC Machine Tools and Basic Manufacturing Equipments"(2010ZX04014-014), Chinese National Natural Science Foundation (51135003,50875039) and Key Projects in the National Science&Technology Pillar Program in the Eleventh Five-year Plan Period (2009BAG12A02-A07-2) as the background, and take continuum structure as the research subject, proposed a new method of topology optimization; Introducing the concept of stochastic optimization, using stochastic finite element method to operate the stochastic topology optimization; The results indicated the necessity of consider the reliability; Introducing reliability analysis theory, researched the reliability-based topology optimization of continuum structure with normal distribution, arbitrary distribution and under multiple failure modes. The Matlab software is used for the research in this paper. Finally, some problems appeared in this paper are elaborate analyzed and solved. The main research contents are as follows:(1) Proposed the k nearest neighbor method of continuum structure topology optimization. The k nearest neighbor technique of pattern recognition is introduced into topology optimization design field. The initial design domain is regarded as the initial sample space, and the finite element as the sample, take the element stress, element stress sensitivity and displacement sensitivity as the characteristic vectors to describe the element sample. The Euler distance of the characteristic vectors is used as recognition mode. The recognition standard is given to pattern recognition so as to classify the elements. The elements with lower element stress will be deleted. To keep the saved element samples as the new sample space, the re-recognition is conducted and re-classified so as to achieve the purpose of optimized structure. Made discussed and detail analysis at the affections to optimization results caused by design parameters. Researched common problems such as checkerboards mesh and postprocess of topology optimization result, and give the solution measure.(2) Proposed the concept of stochastic topology optimization. Generally, the topology optimization design is to the deterministic parameters. In fact, the parameters of materials, working environment and the load have random parameter. The stochastic finite element method is based on the deterministic finite element method, is more fit the need of actual engineering. Therefore, considering the influence of random parameters to conduct stochastic topology optimization design by stochastic finite element method is necessary. Due to the influence of random parameters, the optimal result of stochastic topology optimization is not certain. This provided an evidence for necessity of considering reliability throughout the topology optimization.(3) Researched the reliability-based topology optimization of continuum structure with normal distribution. Introduced the reliability theory, analyzed the mathematical model and give the method of solution. Established the mathematical model of reliability-based topology optimization design with normal distribution. Using the moment method of reliability theory and finite element method to solve the reliability constraint. The k nearest neighbor method is used to conduct the topology optimization and obtained the optimal results of reliability-based topology optimization.(4) Researched the reliability-based topology optimization of continuum structure with normal distribution. In the cased of the random variables obey arbitrary distribution and unable to standard normal quantification, the first four moments of basic random variables known, established the mathematical model of reliability-based topology optimization, and gives two kinds of methods to solve reliability constraint. Using moment method of reliability theory and finite element method to get reliability index and the reliability constraint is solved by first fourth moment method. The stochastic perturbation method is used calculating the reliability index and probability. Edgeworth series method and Hermite polynomial are used in the proceeding reliability analysis to solve the reliability constraints. Finally we got the optimal results. The comparing of optimal results by two kinds of methods proved the correctness of these two calculating methods.(5) Researched the multiple failure modes reliability-based topology optimization for continuum structure working under multiple failure modes. It is respectively hypotheses that each failure mode is unrelated to other, based on the weak failure mode and the related failure mode. The calculated methods are given to the hypotheses. Detailedly discussed the case of related failure mode. After determine the correlation coefficient matrix, deduced the reliability calculation model of related failure mode based on O.Ditlevsen second order narrow bound theory according to the principle of prominent major failure mode and ignored secondary failure mode. Finally we conducted the reliability-based topology optimization under hypotheses multiple failure modes respectively to continuum structure with normal distribution and arbitrary distribution.