Dynamic Behavior And Optimization For Thin-walled Spherical Shell Structures

Thin-walled spherical shell structures have been widely used in aerospace,aviation, navigation, machinery, chemical industry, construction and otherengineering fields because of their advantages of light weight, high bearingcapability, and the ability of providing security protection space. As a kind ofcollision kinetic energy dissipation structure, its deformation characteristics,crashworthiness and energy absorption capability have also been the focus ofresearchers. In this paper, various forms of thin-walled spherical shell structuresare studied, and numerical simulation of these structures under impact have beencarried out to discuss the characteristics of deformation and dynamic response ofthin-walled metal hollow sphere and double fluid-filled hemispherical shell, thenoptimize the single layer thin-walled shallow spherical shell with the sameheight and the double liquid-filled hemispherical shell with different liquidheight. The specific contents are as follows.Numerical simulation has been performed to investigate the deformationprocess of thin-walled metal hollow spheres with different diameter to thicknessratios under different impact velocities. Their compression process can bedivided into six phases: local flatten, axisymmetric depression, asymmetricpolygonal depression, contact with the inner surface of the hollow spheres andinteraction, sidewall failure, densification. The affection to their deformationprocess of diameter to thickness ratio and impact velocity has also been takeninto consideration. The deformation process of hollow spheres with different diameter to thickness ratios is basically same before the inner surfaces contact,while it will reverse with different directions after the inner surfacescontact.The larger the diameter to thickness ratio, the smaller the contact force,the easier case to form a polygonal depression. Meanwhile, the diameter tothickness ratio has a little effect on the asymmetry of the hollow sphere whencompressed. As the impact velocity increases, the sunken time of the bottom ofhollow sphere is much earlier, the asymmetry is much larger and greater initialpeak contact force will produce.The dynamic response of double layer fluid-filled hemispherical shell withfour kinds of fluid height under impact has been simulated numerically. Theresults show that the form of the deformation can be divided into two types: highfluid-filled case and low fluid-filled case. For high fluid-filled shell, the innershell sunken in the bottom, while it sunken in the top for low fluid-filled shell.Simultaneously, the water pressure-time curves in the top and bottom, contactforce-time curves and energy absorption have also been analyzed. As the heightof fluid increases, the peak water pressure in the bottom gradually increases, andthe peak contact force also increases. The impact energy is mainly absorbed bythe outer shell, and the inner shell also absorb certain energy when it sunken,while the energy absorbed by water is negligible.The surrogate model technique based on design of experiment (DOE) andresponse surface method (RSM) is the main method to optimize crashworthinessof thin-walled structures. In the paper, common crashworthiness criterions aredescribed briefly, flowchart and mathematical models of multi-objectivecrashworthiness optimization are given, and some common design ofexperiment methods are introduced. Finally, the basic theory of RSM andcommon multi-objective optimization methods are statement detailed.Based on the theories above, multi-objective crashworthiness optimizationof single layer thin-walled shallow spherical shell with the same height has beencarried out. During the optimization, the curvature radius and thickness of spherical shell are selected as design variables, and peak crushing force, specificenergy absorption and displacement of vertex are set as the optimizationobjectives. During the optimization, a comparison is made between four kinds ofclassical multi-objective optimization method (namely the linear weighted summethod, ideal point method, geometrically averaged cost function method,multiplication and division method), and one kind of heuristic multi-objectiveoptimization algorithm (namely the Non-dominated Sorting Genetic Algorithm,NSGA-Ⅱ). Pareto optimal solutions of multi-objective optimization problemare obtained. The Optimization results show that heuristic multi-objectiveoptimization algorithms can get the optimal solution set for multi-objectiveoptimization problem, but the classical methods can only get an optimal solution.When knowing each target preferences, the classical methods can also getreliable optimal results.The multi-objective crashworthiness optimization for the two forms ofdouble fluid-filled hemispherical shell has also been carried out. During theoptimization, the mass of spherical shell and the outer shell radius are constant.Height of the fluid and thickness of the inner shell are selected as designvariables. Displacement of vertex, peak crushing force and specific energyabsorption are set as the optimization objectives. NSGA-Ⅱ is used to optimizethe design, and the Pareto optimal solutions are obtained.