Time-domain Dynamic Topology Optimization Considering Self-weight Loading Of Functionally Graded Material Structures

Dynamic behavior and structural self-weight are important factors to be considered in structural optimization design in the field of mechanical engineering,ship,aerospace and so on,especially for mechanical structures with non-uniform distribution of materials such as Functional Gradient Materials(FGM).The performance of FGM can vary in one or more directions with more design freedom and better mechanical properties compared with traditional homogeneous materials,which are widely used in mechanical field.Based on this,a time-domain dynamic topological optimization method for functionally gradient material structures with self-weight load was developed.A structure redistribution strategy for FGM-SIMP gradient materials was presented in the framework of Solid Isotropic Material with Penalization(SIMP).In addition,The dynamic structure optimization formulation was established with minimum dynamic flexibility as optimization objective and structural volume as constraints.Based on the adjoint method,the sensitivity was derived in the time domain and solved by the MMA(The Method of Moving Asymptotes)method.Through two-dimensional and three-dimensional typical numerical examples,the dynamic topology optimization design of homogeneous material structures and FGM Structure with self-weight load are systematically studied,and the effects of loading time and the ratio of external load to self weight load on the final configuration of homogeneous material optimization are deeply analyzed.Meanwhile,the influence of self-weight load and material gradient distribution direction on FGM optimization results were systematically analyzed.Finally,the validity of the proposed method was verified by numerical simulation and experimental test methods for homogeneous materials(a special case of FGM).The proposed work can provide some guidance for the consideration of self-weight in the design of dynamic structures of homogeneous materials and FGM.The main research work is as follows:(1)A time-domain dynamic topology optimization method with self-weight was proposed.Based on SIMP algorithm,a time-domain dynamic topology optimization model with self-weight load was established.A polynomial material interpolation penalty model was introduced to provide non-zero stiffness when the intermediate density tends to zero,and a uniform material self-weight load distribution mode in which the units were evenly distributed to the nodes was introduced.In order to select reasonable parameter values of Newmark dynamic solution method,the optimization results of different parameters were compared and analyzed.Considering the self-weight load of structure in time-domain dynamic topology optimization method,a time-domain dynamic topology optimization model with volume constraints and minimum structural dynamic flexibility under self-weight load is established,and the objective function and sensitivity formula are derived.Reasonable parameter values are determined by analyzing the influence of different parameters of Newmark method on the optimization results.At the same time,the results of static and dynamic topology optimization considering the self-weight load were compared,and the influence of different loading time on the results of dynamic optimization is also discussed.In addition,the static and dynamic results of topological optimization with self-weight load and the influence of different loading time on the results of dynamic optimization are compared.In particular,the different ratios of external load to self-weight load and the effects of with/without self-weight on the optimization results were systematically analyzed.Finally,the validity of the method was verified by a number of two-dimensional and three-dimensional examples.(2)A time-domain dynamic topology optimization method for functionally gradient material structures with self-weight load was presented.In the framework of SIMP,a strategy of structural self-weight distribution for FGM-SIMP was proposed and a time-domain dynamic topology optimization model for FGM structure was established.The topology optimization design of FGM structures with self-weight loads were studied through several typical numerical examples in two and three dimensions and the influence of self-weight loads and the direction of material gradient distribution on the optimization results of FGM structures were discussed in detail.It is found that the self-weight load and the distribution direction of material gradient have a great influence on the optimum configuration and dynamic stiffness of FGM structure.To further explore the influence of non-uniform distribution of FGM material components on the optimization of final configuration,the optimization results with different volume/mass constraints and different constraints ratios were systematically studied.It is found that material distributions with the same FGM structure show opposite trends with different volume/mass constraints.Especially with the increase of restraint ratio,the target function with/without self-weight also shows the opposite trend.(3)Sample preparation,dynamic experiments and numerical simulation studies with and without self-weight loads were carried out.To further verify the validity of the proposed method,taking homogeneous material(special case of FGM)as an example,the CAD geometric reconstruction model of the optimized structure with/without self-weight load was carried out,and then the dynamic simulation analysis was carried out by using the Abaqus steady-state dynamic module.By comparing the first four natural frequencies of the two optimized structures,it is found that the natural frequencies of the optimized structures considering self-weight are significantly increased,especially the first natural frequency is increased in engineering,so that resonance of the structure can be avoided to a certain extent.The simulation and experiment results show that they are in good agreement,which verifies the accuracy of the numerical simulation model.In addition,the experimental results show that the displacement amplitude of the optimized structure considering self-weight is smaller.It is proved that the optimized structure obtained by the proposed method has higher stiffness.Based on the validated numerical simulation model,the dynamic simulation analysis of several groups of numerical examples is carried out,and the dynamic characteristics of the structure with/without self-weight load optimization are systematically analyzed,which further verifies the effectiveness of the proposed method.