Research On Design Method And Application Of Reliability-based Topology Optimization For Load And Heat Insulation Integrated Functionally Graded Material Structures

The coupling of load and heat conduction is widely existed in aerospace,power machinery,energy and chemical equipment,electronic systems and other engineering fields.The design of mechanical load and heat insulation integrated structure which can meet the requirements of reliability,lightweight,high strength and excellent thermal protection has become a hot and difficult problem.The discontinuity of the linear expansion coefficient of each component material in the functionally graded material structures can be alleviated,so as to realize the effective control of the interface stress and thermal stress.As a result,it has a great application prospect in the mechanical load and heat insulation integrated structure.Topology optimization is an important method of modern structural design.At present,the research on functionally graded material structures mainly focuses on the performance index model and is limited to the deterministic topology optimization design.In addition,there are some problems such as the theoretical system of topology optimization for two types of functionally graded material structures is not perfect,and the design software needs to be developed.Due to the fact that functionally graded material structures are mostly used in severe working conditions in practical engineering,it is easy to lead to structural performance degradation,low safety margin and increasing failure modes by using deterministic model.It is of great theoretical and practical significance to carry out systematic research on functionally graded material structures design based on reliability-based topology optimization theory for improving the theoretical system and servicing engineering application in this field.Based on the theory,simulation and experimental methods,this paper systematically studies the influence mechanism of reliability-based topology optimization efficiency,reliability-based topology optimization theory based on economic index model,functionally graded material structures topology optimization theory and finite element simulation integrated application for topological layout.It is committed to breaking through the technologies such as cost control of reliability-based topology optimization solution,establishment and solution of economic index reliability-based topology optimization model,construction of two material interpolation models,automatic identification of topological layout and automatic reconstruction of finite element mesh model.It also provides theoretical support and feasible solutions for reliability design in conceptual design stage of engineering structure,and independent development of industrial software integrating optimization function.In addition,combined with heat transfer theory,a multi-scale design method of load and heat insulation integrated functionally graded material structures considering both topological layout and material parameters is proposed.By introducing material science theory and machine learning algorithm,the prediction method for mechanical property and heat transfer performance of functionally graded material structures are used to verify the theoretical model and design method.The main research work and innovation of this paper is divided into four parts.(1)Reliability-based topology optimization method based on Independent Continuous Mapping method and its simulation and experimental researchFirstly,the traditional deterministic economic index model is improved based on the optimization efficiency influence mechanism of Independent Continuous Mapping method.Secondly,combined with the first-order reliability method,an efficient reliability-based topology optimization model with quality as the optimization objective and displacement as the constraint is established,which can effectively control the calculation cost from two aspects of solution strategy and topology optimization algorithm.Compared with the existing performance index model and the traditional economic index model,the optimization efficiency of the modified model can be improved by 44.59%and 64.76%respectively.Finally,the strength and stiffness of the hollow plate structure designed by the modified model are evaluated.Compared with the traditional structure,the strength and stiffness of the new structure were increased by 60.88%and 55.30%respectively.Furthermore,the first-order natural frequency and stress mode are significantly improved as well.Based on the results of numerical calculation,simulation and test,the validity of the theoretical model is verified.(2)Topology optimization design method,simulation and experimental research on load and heat insulation integrated functionally graded material structuresFirstly,for two kinds of functionally graded material structures,including multi-layer variable stiffness and continuous gradient stiffness structure,the material interpolation models of Lagrange interpolation polynomial and binary exponential gradient coefficient function are constructed respectively.Secondly,the material interpolation model is introduced to establish a functionally graded material structures topology optimization model with mass as the optimization objective and displacement as the constraint,and the influence of displacement constraint and gradient coefficient combination on the optimization results is explored.Finally,based on the theory of heat transfer,a multi-scale design method of functionally graded material structures considering both topological layout and material parameters is proposed.In addition,combined with composite material science theory and machine learning algorithm,a prediction method of mechanical property and heat transfer performance of functionally graded material structures is established,and applied to sandwich structure design and performance evaluation.According to the simulation results,compared with the traditional homogeneous core sandwich structure,the thermal insulation and thermal stress relaxation performance of the new structure with the same bearing capacity can be improved by 86.50%and 42.10%respectively,and the experimental results are in good agreement with the simulation,which verify the validity of the theoretical model and design method in this paper.(3)Research on reliability-based topology optimization design method of load and heat insulation integrated functionally graded material structuresFirstly,in view of the fact that functionally graded material structures are mostly used in severe working conditions,and there are many uncertain factors in the design,manufacturing and working.Combined with the theoretical models that have been verified in the first two parts of this paper,a reliabilitybased topology optimization design method of graded material structures based on economic index model is established,and the influence of displacement constraints,gradient coefficient combination and reliability index on the optimization results are explored.Furthermore,the method is applied to the multi-scale design and performance evaluation of load and heat insulation integrated functionally graded material structures considering reliability,mechanical properties,lightweight and thermal properties.According to the simulation results,compared with the traditional homogeneous core sandwich structure with the same bearing capacity,the thermal insulation and thermal stress relaxation performance of the new structure are improved by 36.30%and 8.60%respectively,which verify the validity of the theoretical model and design method in this paper.(4)Development of finite element simulation integrated application for topological layoutFirstly,the topology optimization design function of the existing computer aided engineering software is developed based on the deterministic theory.In order to solve the reliability design requirements in the conceptual design stage of engineering structure,a new method of automatic topological layout identification and finite element mesh model reconstruction is developed.Secondly,through the development of an finite element simulation integrated system for topological layout,which has the main functions of topology optimization design,node automatic numbering,element automatic numbering,topological layout automatic identification,finite element mesh automatic reconstruction,finite element mesh file automatic generation,etc,the control of engineering design cycle,geometric model reconstruction and structural performance analysis precision can be realized.Furthermore,it can also realize the integrated application of the optimization design theory and the analysis functions of statics,heat transfer characteristics and thermal stress relaxation performance in the existing computer aided engineering software.Finally,the validity of the system is verified by a test example.