Research On Topology Optimization Of Continuum Structures And Design Of Compliant Mechanisms With Uncertainty

A large number of uncertainties exist in the actual engineering, and these uncertain factors should be considered in structural or mechanism design. Topology optimization of continuum structures and designing of compliant mechanisms with uncertainty have wide engineering background and are of important theoretical significance and research worthiness.Some researches on special topics are presented in this dissertation, which include the static and dynamical characteristic analyses, the probabilistic and non-probabilistic reliability and robust topology optimization of continuum structures with random or interval parameters, the designing of fully and hinge compliant mechanisms with random or interval parameters. The main research works can be described as follows:1. The problem of topology optimization with stress constraints of planar elastic continuum structures under random loads are investigated, in which the structural parameters are random variables. The topology optimal model is constructed based on probability. The probabilistic stress constraints are transformed into equivalent normal constraints. The computational expressions of numerical characteristics of stress responses are deduced. The corresponding solving method is proposed.2. Dynamic characteristic topology optimization about continuum structure with random parameters is investigated based on frequency probability constraints in this paper. Basing on frequency probability constraints, the models of topology optimization about bending thin plate and plain stress thin plate are constructed. The numerical characteristic of structure with random parameters is deduced by transforming frequency probability constraints into equivalent normal constraints. A new evolutionary optimal criterion is proposed.3. Considering the random uncertainties of elasticity modulus and mass density, the mathematical model of robust topology optimization of vibrating structures is proposed, in which the desired eigenmode shapes are utilized as objectives. The summation weighting coefficient is introduced to build the objective function including the mean value and the standard deviation of the original one, and the standard deviation of original constraints and the probability index of the constraints satisfaction are introduced to build the new constraint functions. The mean value and the standard deviation of objective function and constraints are obtained by Monte Carlo simulation. The sensitivities of objective function and constraints are calculated, based on which the Sequential Linear Programming method is used to solve the optimization.4. The present paper is concerned with topology optimization of planar continuum structures with interval parameters subjected to non-probabilistic constraints on fundamental eigenfrequency and the forbidden zone between two eigenfrequencies. Considering the interval uncertainties of elasticity modulus, mass density and also...