| With the rapid development of the global economy,the efficient use of resources is facing great challenges.On the other hand high-performance engineering structure requires fine design,leading to the urgent need to explore the design methods which can produce lightweight,environmentally friendly and high performance structures.Among them,the continuum topology optimization method is widely used in all walks of life because of its design of multiple degrees of freedom,engineering application potential and so on.The uncertainty in the applied load is the inherent property of the actual engineering structure,which usually has a great influence on the structural performance.However,the existing robust topology optimization methods are inefficient in solving the design problem in presence of uncertain applied loads,and do not consider the subjective uncertainty information.Therefore,it is of great significance to develop the continuum robust topology methods considering the uncertainty in applied loads.Based on the in-depth study of the continuum topology optimization methods considering uncertainties,in view of the key problems for existing RTO methods considering uncertain applied loads,this thesis mainly study efficient stochastic RTO method,RTO method considering subjective uncertainty information,efficient interval RTO method,and avoid non-support optimization design.The effectiveness of the proposed methods is verified via benchmark numerical examples.The main research work is as follows:(1)An efficient robust continuum topology optimization method by considering the stochastic uncertainties in the applied loads is proposed.Uncertain load vectors are dealt with by using additional uncertain pseudo random load vectors.The expectation and the variance of the strain energy are expanded by using Taylor expansion technique,respectively,and their linear terms are respectively chosen.The mathematical model for the robust topology optimization is established by minimizing the weighed linear terms of the expectation and the variance of the strain energy,while restricting the material volume.At the same time,a dimensionless coefficient is introduced to balance the units between the expectation and the variance.The sensitivity is derived by using the adjoint method.Then,the design problem is solved by the simple yet efficient bi-directional evolutionary structural optimization method.Finally,the effectiveness is demonstrated by several benchmark numerical examples.(2)A robust continuum topology optimization method in consideration of the subjective uncertain information is developed.The cloud model is employed to characterize the probabilistic and fuzzy uncertainty of the directions of the applied loads.Each cloud drop represents one applied load may appear.The robust topology optimization problem is equivalently transformed into a deterministic topology optimization problem with multiple load cases.Since a large amount of cloud drops are needed to construct the cloud model to ensure that the optimal solution is achieved,and the number of the cloud drops is equal to that of the load cases,so the algorithm is very inefficient.By defining the virtual applied load,an efficient strategy is put forward,which significantly improve the efficiency of the algorithm.The design problem is solved by the improved bi-directional evolutionary structural optimization method using the derived sensitivity numbers.Finally,a series of numerical examples have revealed the effectiveness of the proposed method.(3)A robust continuum topology optimization method in presence of uncertainties in the locations of the applied loads is presented.The subjective uncertain information of the designer is taken into account.The cloud model is extended to characterize the uncertainties in the locations of the applied loads.Every cloud drop means the possible location of the applied load.The robust topology optimization problem is equivalently transformed into a deterministic topology optimization problem with multiple load cases.As a mass of cloud drops are needed to construct the cloud model to guarantee the optimal solution,and the number of the cloud drops equals that of the load cases,resulting in the algorithm inefficient.In order to improve the efficiency of the proposed algorithm to make it more suitable for engineering applications,an efficient strategy is proposed.In the framework of the bi-directional evolutionary structural optimization method,the design problem is solved efficiently by utilizing the derived sensitivity numbers.The validity of the algorithm is verified by benchmark numerical examples.(4)A simple yet efficient robust continuum topology optimization method is proposed by considering the interval uncertainties in the directions of the applied loads.The uncertain load is characterized by the mathematical model when it can not be accurately measured by the random or fuzzy mathematical models.The interval mathematics theory is used to approximately convert the robust topology optimization problem into a deterministic one with multiple load cases.An efficient strategy is introduced to improve the computational efficiency of the proposed algorithm.The design problem is solved via the improved sensitivity numbers.Finally,the effectiveness and efficiency of the proposed algorithm are highlighted by the use of benchmark numerical examples and Monte Carlo methods.(5)A simple strategy is presented to avoid the non-support topology optimization design when a structure is subjected to self-balance applied loads.The design conundrum is systematically demonstrated by a series of two-dimensional cantilever beam and a practical engineering structure design examples,and a alternatively scheme is suggested to tackle such a conundrum.The optimal layouts of the cantilever beams after the scheme implemented is fabricated by 3D printing method,and simple mechanical tests are then conducted for them,indicating that the suggested scheme has successfully handled the non-support topology optimization design problem. |
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