A Temporal Stable Nodal Integration Method And The Application In Magnetic-mechanical Coupling Problem

Magnetic-mechanical coupling problems are quite common in practical engineering,and numerical simulation of these large scale and complex problems which cover electromagnetic field computation and dynamic large-deformation analysis such as electromagnetic forming(EMF)wins the concern of engineers and researchers recently.It is tough to use traditional numerical simulation methods to solve this kind of problem.Finite element method(FEM)with linear triangular or tetrahedral element is convenient for mesh generation and numerical computation,and is suitable for complex problems.However,the relatively poor accuracy and the low ability to handle mesh distortion remain the headache problems for this formulation.The meshless methods developed in recent twenty years still can not be applied widely to solve complex problems for their high cost of calculation.How to take the advantages of unstructured mesh to construct high accuracy,low computation cost and low mesh dependent algorithm is the key issue to solve magnetic-mechanical coupling problems.Therefore,to satisfy the demand,this work presents a temporal stable nodal integration method which contains the attracting features of both FEM and meshless methods.The performance of this method in accuracy,efficiency,stability and convergence for mechanical field analysis and electromagnetic field computation has been examined through corresponding numerical examples.Finally,the developed algorithms are used to solve EMF and electromagnetic riveting(EMR)problems.The dissertation includes the following aspects:1.A temporal stable nodal integration method(SNS-FEM)is proposed.To cure the instability of traditional node-based smoothed finite element method(NS-FEM),this work formulates a stable nodal integration method by incorporating strain gradient terms into the calculation of strain energy,and then the method is adopted to solve elastic static and dynamic problems in two and three dimensions.Using this formulation,the low pre-processing cost and simplicity for computation of unstructured mesh are maintained,and the accuracy of traditional FEM is effectively increased.And also,the particle like property facilitates SNS-FEM the convenience for post-processing,data transmission or coupling with other methodologies.The computation accuracy,efficiency,stability and convergence of the proposed formulation are studied through detailed analyses of benchmark cases and practical engineering problems.And it is found that SNS-FEM can offer high accuracy results,and the spurious non-zero energy modes of original NS-FEM can be eliminated effectively.2.The stable nodal integration method for dynamic large deformation analysis is proposed.In large deformation cases,the instability of NS-FEM is quite prone to be excited and leads to spurious modes,and the construction of stabilization terms for implicit elastic problem can not be applied directly to explicit non-linear problems.This work incorporates the strain variant terms into the calculation of internal force and formulates the integration scheme for explicit dynamic analysis.Performance of the proposed method is examined through numerical examples such as extrusion and impact.It turns out that SNS-FEM solution has favorable characteristics including:less integration points,which is quite competitive in explicit problems;insensitive to mesh distortion and can continue to compute even when the deformation is really distracted;and the computation accuracy is increased in the same way.3.The stable nodal integration scheme for solving electromagnetic problems is formulated.The electrostatic,magnetostatic,quasi-static eddy current and transient eddy current problems are studied respectively,and the derivative terms of shape function are expanded as the first order Taylor form to formulate the stable nodal integration method in each case.The proposed method is derived based on linear triangular or tetrahedral mesh,and its basic principle,final equation form and the program implementation are fairly easy.Efficacy of the proposed method is examined through several benchmark numerical examples.The formulated solution increases the computation accuracy with unstructured mesh,so it has advantage in complex problems.4.Based on the proposed nodal integration method,the efficient and automated computation platform is constructed and then used to simulate EMF and EMR processes.The corresponding high efficient algorithm is adopted for each modulus of the platform considering features of the method,and iterative coupling strategy is used to simulate the interaction between different physical fields.A weighted elastomer method is adopted to accomplish the mesh updating in iterative coupling simulation.The weighted elastomer method do not add extra nodes and maintains original topological relation of the mesh,so it is an simple and effective mesh update method with high adaptability.The actual effect in computation accuracy,efficiency,and stability of proposed methods is examined through analyzing tube bulging,tube compression,and riveting of aluminum alloy materials.Adoption of the developed computation platform has the following advantages:(1)there is no need of crosscalling between various softwares,and manual interventions are completely avoided during the computation,so the simulation can be realized automatically with one input file in the specified format;(2)the fully coupling between various physical fields is accomplished;(3)the platform is suitable for complex structures since it is established based on linear triangular background mesh;(4)rather competitive computation accuracy and efficiency are obtained by nodal integration method,so it has application value in actual engineering problems.