Optimization Design For 3D Random Structures Based On Dynamic Characteristics Reliability Constraints

In many practical engineering structures, when external or internal mechanical excitation frequency is very close to the natural vibrant frequency of structures, amplitude of structural vibration will be enlarged, which inevitably affects the structural safety and function. How to avoid resonance and decrease the amplitude of structural vibration by using structural optimization design is significant in view of both theoretical study and practical utilization. In this paper, considering the randomness of structural materials parameters (such as elastic modulus), a new method combining with recursive stochastic finite element method and the design point method of the structural reliability is used to study the dynamic reliability of stochastic structures and structural optimization design based on the dynamic reliability constraints. The main research works can be described as follows.1. Induce and summarize the research of reliability problems and structure optimization design based on reliability involving random variables both at home and abroad; Introduce stochastic finite element method in detail and its various algorithms at detail; The results obtained utilizing RSFEM are proved to be rationality and the validity.2. Based on the RSFEM, a new computational method of dynamic characteristics reliability index is proposed. In the example of the 3d spatial cantilever beam, the results obtained using the new method have a well agreement with Monte-Carlo simulation results, and the proposed algorithm can save much calculation time.3. Regarding the sectional sizes as design variables, a new dynamic characteristics reliability optimization method of random structures is developed. In optimization models, the structural total weights are defined as objective functions and dynamic characteristics reliability are included in constraint conditions. The dynamic characteristics reliability constraints and their simplification expressions are analyzed. Then sequential quadratic programming (SQP) method is applied to realize structural optimization. From two examples, it can be found that the results of deterministic deterministic structural optimization can not satisfy the dynamic reliability constraints of stochastic structures.