Research Of Energy Equivalent Static Load Method Based On Critical Time Point And Structure Dynamic Response Optimization

Traditional structural optimization is carried out under static load, while mechanicalstructure of engineering practice was generally under locally dynamic load, therefore theresults based on static structure optimization design method cannot meet the requirements ofthe structural dynamic performance. Due to the time-related dynamic constraint of the directdynamic response optimization technology was difficult to deal with, the direct optimizationcalculation of dynamic response is large scale and difficult to converge, so it is not feasiblefor structural dynamic response optimization design directly in engineering applications.Therefore, it is considered to transform dynamic load into equivalent static load. At present,the Equivalent Static Load method based on displacement, transforms dynamic load intostatic load via equivalent displacement, and further transforms the structure dynamic responseproblem into structure static response problem. This method takes the maximumdisplacement point as the equivalent transformation time point, without considering thedynamic response of the maximum stress time point, and cannot fully reflect the dynamicperformance of the structure, and the equivalent transformation critical time point is difficultto identify. Whatever, the equivalent static load method based on displacement is short incomplex computation and insufficient optimization inefficient, which leads to poorpracticability? In addition the current dynamic response optimization is based ondisplacement, ignoring the effects of stress response on the structural dynamic performance.Aiming at the problem that the critical time point at which the structure dynamic loadequivalent transformation is taken was difficult to identify, a method based on discretizingthe solution space of the dynamic response by the spectral element method to identify the critical time point is presented. The paper utilizes the discrete by spectral element method andthe high-precision of the Gauss–Legendre–Lobatto (GLL) point interpolation, calculatesthe spectral element discrete solution space of the structure dynamic response (stressresponse and displacement response included) resulting from the modal superposition methodcalculation, and obtain a high-precision interpolation function of dynamic response timehistory, by Lagrange interpolation at GLL point, constructed a mathematical model toidentify the structure of the critical time point under dynamic load, and get the absolutemaximum structure dynamic response value point by global optimization algorithm (DIRECTmethod), called critical time point. Finally, a124-plane truss and cantilever beam were takenas examples to demonstrate the effectiveness of this method.Aiming at the complex optimization calculation and poor practicability of the EquivalentStatic Load method based on displacement, a method in which the dynamic load istransformed into static based on energy principle is presented. This method is based on theconservation of the energy before and after the load equivalent, constructs a mathematicalmodel of the transformation of the dynamic load into static load, and obtains the equivalentstatic load set by global optimization algorithm (DIRECT method) eventually. The124planetruss was analyzed as an example, to confirm the validity of this method.Aiming at the insufficiency of simply considering the displacement response when thestructure is dynamic optimized by using the Equivalent Static Load method based ondisplacement, a structure dynamic optimized design method based on system response ispresented. The structure is optimized with the displacement response and the stress responsewhich are generated when the structure is under dynamic load, as constraint functions of theoptimization model, and the static load set, which is generated by equivalently transformationat critical time point identified from the point of stress and displacement, as the external loadcondition of structure dynamic optimization. A circular hollow section beam, a3-trussstructure, and a10-truss structure were taken as examples and compared with the literatures.The results show that, the optimization result obtained by this method is more accurate. A diesel engine piston was used as the application study in this paper. The thermalboundary condition of the piston was corrected by the test results, and the temperature ofeach node of the piston was got by the finite element method. The dynamic response solutionspace of the piston was got by the thermo-mechanical coupling static analysis and thetransient kinetic analysis of the piston. The method to identify the critical time point and theEquivalent Load method based on energy principle presented in this paper were used totransform the dynamic load into static load equivalently at the critical time point, and then thestructure optimization design method based on system response was applied. Theoptimization of the dynamic response of the piston was achieved eventually, and achievedgood results.By the investigation of the energy principle based Equivalent Static Load method and itsapplication for the dynamic response optimization in the paper, breakthroughs in the areas ofthe identification of critical time point of the transformation of equivalent load, thetransformation of dynamic load into static load based on energy principle and the structuredynamic response optimization design based on system response, are made, and a series ofconclusion and results with theoretical significance and practical value are received. Thepaper expands the scope of the theoretical study of Equivalent Load method, and opens a newway of theoretical study on dynamic response optimization theory.