Research On Dynamic Simulation And Shape Optimization Of Hyperelastic 3D Models Based On Isogeometric Analysis

Physical based dynamic simulation is one of the research hotspots in the field of graphics.It is widely used in industrial manufacturing,computer animation,games,and other fields to provide users with authentic and reliable physical simulation results.Finite element analysis is one of the most commonly used methods for solving physical equations,and the accuracy of its solution is affected by the mesh quality.However,the mesh is susceptible to distortion and deformation when the hyperelastic model is in movement,which directly influences the accuracy and speed of the simulated result.The solution to this problem is usually to re-mesh the model after movement,but the frequent division operations increase the computational cost.Thus,physics-based hyperelastic dynamics simulation needs a method that balances numerical accuracy and simulation speed.In this thesis,we propose a dynamics simulation method for hyperelastic material models based on isogeometric analysis to realize the dynamics simulation of complex 3D models.Moreover,based on the simulation,this thesis proposes a shape optimization method for hyperelastic materials based on isogeometric analysis to improve the optimization quality.The main contributions of this paper are summarized as follows.1.A framework for the dynamics simulation of hyperelastic materials based on isogeometric analysis is proposed.The method first derives the linearized form of the hyperelastic constitutive model by geometric boundary conditions and material parameters.Secondly,the computational domain space is discretized using the isoparametric idea to establish the discrete equilibrium equations under the isogeometric method.Then the iterative form of the equations is formulated by combining the incremental method to establish the nonlinear solution system and derive the solution procedure.After substituting the Lagrangian kinetic equations,the time domain is discretized using the implicit time integral to obtain the iteration relationship in time step order.Finally,the nonlinear system is solved in each time step to obtain the numerical solution of the simulation.The stability and accuracy of the method are verified through the experimental analysis and comparison of complex 3D models.2.A more widely applicable isogeometric analysis of the hyperelastic material shape optimization method is proposed based on the hyperelasticity simulation framework.Firstly,this paper constructs various objective functions and constraints.Then we derive the sensitivity calculation formulae for each objective and constraint.Secondly,the analytical model and design model sensitivity transfer methods are constructed to improve the accuracy of the simulation calculation during the optimization process.Finally,this paper conducts optimization tests on a variety of 2D and 3D models and compares the optimization results with those of linear elastic materials to verify the reliability and effectiveness of the isogeometric analysis hyperelastic material optimization method.