Research On Complex Dynamic Problems Based On Efficient Finite Element Method

Advanced electronic technology has increasing requirements for the performance of electronic devices,and traditional design methods of electronic devices have been unable to meet the requirements of high density,high performance,and high reliability in current electronic devices.In order to design the optimal electronic devices from the overall performance,in addition to ensuring the performance of the main electrical parameters,the reliability of heat dissipation and vibration needs to be analyzed.In other words,we must fully consider the displacement field of structure,temperature field,electromagnetic field,flow field,etc.Displacement field of structure plays a vital role in performance analysis of electronic devices.On the one hand,in order to design electronic devices with high reliability and stability,it is necessary to understand their instability in current designs,which is important in the design of electronic devices.On the other hand,under external load,the boundary conditions of the electromagnetic field are changed due to the deformation of the key structure of the electronic devices,which will affect the realization of electrical performance.Using simulation technology to analyze the reliability and displacement field of electronic devices in advance is an economical and effective way.Therefore,it is necessary to develop a CAD/CAE integrated rapid design system of dynamic analysis for electronic devices.In this dissertation,a software of MCS for dynamic analysis of electronic devices has been developed and presented,which provides an effective simulation tool for the structural reliability of electronic devices and the pre-analysis of displacement fields.The research work focuses on the CAD/CAE integrated design environment,accurate and fast vibration analysis,accurate and efficient solution technology of flow field,and fluid-structure coupling technology.The main contributions are as follows:1.A 3D dynamics simulation software based on finite element method is developed.The software is implemented in C ++ programming and includes four modules: solid modeling,meshing,dynamics simulators,and post-processing.Among them,solid modeling supports fast modeling and parametric modeling.Meshing supports tetrahedral mesh,curved mesh,boundary layer mesh,mixed mesh,etc.,and has local encryption function.The dynamic simulators include free vibration analysis,random vibration analysis,flow field analysis,and static analysis module for auxiliary flow field analysis.The post-processing module has three-dimensional field,two-dimensional surface field,and curve display functions.The software can be used to realize the pre-analysis of the structural reliability and displacement field of electronic devices.2.A CAD/CAE integrated rapid redesign system of vibration analysis with a unified data architecture is proposed.This system can shorten the cycle of the design-analysis-redesign procedures.In this design system,designers can quickly and freely complete component design and performance analysis without using two different software or two interface environments.The numerical experimental results show that the analysis and design efficiency of MCS software is higher than that of commercial software while ensuring the calculation accuracy.3.An improved implicit restart Lanczos iterative method is proposed for free vibration analysis,and random vibration analysis is realized in combination with pseudo excitation method.The improved implicit restart Lanczos iterative method transforms the problem of solving natural frequency in the low frequency band to the iterative solution in the high frequency band by introducing a spectral transformation.This method only needs to make a preconditioner once before Lanczos iteration.Pseudo excitation method is applied to random vibration analysis based on mode superposition scheme,which improves the efficiency of vibration analysis.The numerical experimental results show that the method proposed in this dissertation comprehensively surpasses the traditional Lanczos iterative method in terms of computational performance,and its performance is better than the commercial software ANSYS.4.A fast solution technology for large-scale linear systems based on three-level preconditioner is established.According to the concept of multi-level preconditioner,a three-level preconditioner for PCG method is proposed.The preconditioner includes a p-type multigrid preconditioner based on higher-order hierarchical basis functions,a MFBIC preconditioner based on processing sickly sparse linear system,and a block Jacobian preconditioner based on three direction components of displacement.The numerical experimental results show that the technology of fast solving proposed in this dissertation has the same accuracy as basic method and commercial software,and has high-efficiency performance and low memory requirements.5.The curvilinear DG method for flow field analysis and fluid-structure coupling method are established.First,the governing equations of the flow field and the DG method are briefly described.Then,the geometric transformation from the real curve element to the standard reference element is studied.Based on the contravariant velocities,a universal implementation of wall boundary conditions and HLLC flux format in curved mesh are proposed.These techniques do not require complex geometric boundary information and are easy to implement.The numerical experimental results show that the curvilinear DG method can obtain reasonable accuracy on appropriately coarse unstructured meshes.Finally,combined with the static analysis,the fluid-structure interaction analysis is preliminarily achieved.6.A highly efficient curvilinear DG method is proposed.First,based on the geometric relationship between convex and concave curved elements and tetrahedral elements,a modified curvilinear DG method is proposed by using the smoothness of the numerical solution,which does not require the integration of the curved element.Then based on the normal vector of geometric boundary and surface Jacobian,a new modified curvilinear DG method is proposed.In the new modified curvilinear DG method,not only integrals over any curved element are avoided,but also the line and face integrations along the curved boundary are not required.The numerical experimental results show that the new modified curvilinear DG method has the same high-order accuracy as the ordinary curvilinear DG method.