Research On Topology Optimization Design Of Uncertain Continuum Structures

There are a large number of errors and uncertainties in practical engineering structures, which cause the physical parameters, geometrical parameters and loads to be uncertain. Therefore, topological optimization designs with these uncertainties are put forward by numerous scholars, and get more and more attentions in academic and engineering kingdom. However, most of topology optimization designs for continuum structures belong to determinate structural optimization design, that is, all the structural parameters are regarded as determinate without considering influence of uncertainties. Obviously, the deterministic models are unable to reflect the influence of uncertain structural parameters on design performances. Consequently, topology optimization designs of continuum structures with uncertainties have wide engineering background, important theoretical meanings and academic values. Studies on topology optimization design of continuum structures with uncertainty parameters are made in this dissertation. The main research work can be described as follows:1. Topology optimization design problem for planar continuum structure with randomness of both geometry and physical parameters under the structural total strain energy constraint is studied. Mathematical model of topology optimization design of random structure is established, in which the minimum mean of structural weight is taken as objective function, the structural shape topology information is taken as design variables, and the probabilistic reliability index of structural total strain energy is taken as constraint condition. The computational expressions for mean value and mean variance of the structural strain energy response are presented by the random factor method and algebra method. The corresponding solving method is proposed.2. Dynamic characteristic topology optimization of continuum structure with randomness of both geometry and physical parameters is researched based on natural frequency probability constraints. Mathematical model of topology optimization design about plain stress thin plate is established, in which the minimum mean of structural weight is taken as objective function, structural shape topology information is taken as design variables, and the probabilistic reliability index of structural natural frequency is taken as constraint condition. Similarly, topology optimization design problem for three dimensional structures with randomness of physical parameters under structural frequency constraints is studied. The numerical characteristics of structure with random parameters are deduced by the algebra method. Meanwhile, the evolutionary structural optimization method is used in the optimization.3. Topology optimization designs of planar continuum structure with fuzzy parameters under fuzzy loads are discussed. Fuzzy variables are transformed into random variables by information entropy. Mathematical model of topology optimization of continuum structures with random parameters under random loads is established. The minimum mean of structural weight is taken as objective function; the structural shape topology information is taken as design variables; and the probabilistic reliability index of structural natural frequency is taken as constraint condition. The element stress constraints are transformed into equivalent normal constraints. The computational expressions of numerical characteristics of stress responses are presented based on random factor method. Bi-directional evolutionary structural optimization method is used in the optimization.4. Topology optimization design of planar continuum structure under interval loads is discussed considering interval uncertainties of physical parameters. The topology optimization mathematical models with stress (structural strain energy) constraints of planar continuum structures under interval loads are established. The minimum mean of structural weight is taken as objective function, the structural shape topology information is taken as design variables, and the non-probabilistic reliability index is taken as constraint condition. Computational expressions of numerical characteristics of stress (strain energy) based on interval factor method and interval arithmetic rule are deduced. Bi-directional evolutionary structural optimization method is also used in the optimization.5. In consideration of structural physical parameters and applied loads being random or interval, random variables and interval variables are transformed into each other by 3σcriteria. For interval parameters structures, the computational expressions of numerical characteristics of node displacement, element stress and strain energy responses are deduced based on the interval factor method. For random parameters structures, the computational expressions of numerical characteristics of element stress, node displacement and strain energy responses are presented based on the random factor method and interval arithmetic rules. Then the static analysis problem of random-interval parameters continuum structures is solved.6. According to the above results, topology optimization design of planar continuum structure with mixed parameters is studied. Firstly, the optimization problem of fuzzy-interval parameters structures under displacement constraints is discussed. Interval and fuzzy variables are transformed respectively into random ones by the 3σcriteria and information entropy. Mathematical model of topology optimization of continuum structures with random parameters is established. The computational expressions of numerical characteristics of displacement responses are presented based on the algebra method. Displacement sensitivity is obtained by unit void load. Bi-directional evolutionary structural optimization method is used in the optimization. Secondly, the optimization problem of random-interval parameters structures under stress constraints is discussed. Interval variables are transformed into random ones by the 3σcriteria. The topology optimization mathematical model is established, taking the minimum mean of structural weight as objective function, the structural shape topology information as design variables, and the stress probabilistic reliability index as constraint condition.