Research On Topology Optimization Of Large-Displacement Compliant Mechanisms With Stress Constraints

Compliant mechanisms is a new type of assembly-free mechanism,which is easy to realize high precision,miniaturization and integrated design and processing.It has been widely used in micro/nano operation,flexible robot and biomedical engineering.With the rapid development of computer technology,topology optimization has become one of the main design methods of compliant mechanisms.Compliant mechanisms usually experience large displacements and large rotational deformations.It is very necessary to consider geometrical nonlinearities for topology optimization of compliant mechanisms.At present,topology optimization of compliant mechanisms mainly based on the linear elastic finite element theory.Therefore,stress-constrained topology optimization of large displacements compliant mechanisms is study in this paper,and the main research contents are as follows:(1)Topology optimization of continuum structures with geometrical nonlinearities.The Total-Lagrangian formulation and the incremental Newton Raphson method were applied to solve the geometrically nonlinear response of the mechanisms.The element energy interpolation scheme for fictitious domain techniques was adopted to circumvent the non-convergence problem in the topology optimization of geometrical nonlinear problems.The minimize of flexibility of structure is developed as the objective function;The volume fraction of structure is developed as the objective function;The optimization model for topology optimization of large displacement compliant mechanism with geometrical nonlinearities was established.The optimization problem solved by the Method of Moving Asymptotes.Numerical examples show that the design method of topology optimization for continuum structures with geometrical nonlinearities based on element potential interpolation is effective.(2)Topology optimization of large displacement compliant mechanisms considering global stress constraints.To avoid static strength failure caused by large deflection,a design method for topology optimization of large displacement compliant mechanisms considering global stress constraints was proposed.The local stresses constraints for all elements aggregated into a global stress constraint using the improved P-norm method.The maximum of the output displacement of the compliant mechanisms was developed as the optimization objective;The volume fraction is developed as the objective function;The optimization model for topology optimization of compliant mechanisms with geometrical nonlinearities considering global stress constraints was established.Numerical examples show that large displacement compliant mechanisms obtained by topology optimization can effectively satisfy the stress constraints.As the allowable stress constraint value decreases,the hinge region in the mechanism configuration expands gradually,which makes the flexibility distribution more uniform,but the output displacement decreases gradually.(3)Topology optimization of multi-material compliant mechanisms with geometrical nonlinearities based on stacking element method.Considering the material boundary conditions,the element stacking method was used to construct the element stiffness matrix of the multi-material structure.The maximum of output displacement of compliant mechanisms is developed as the objective function and the volume fraction of each phase material is developed as the constraint conditions;The topology optimization model of the multi-material compliant mechanisms with geometrical nonlinearities based on the stacking element method was established.Numerical examples verify the effectiveness of the proposed design method.In order to meet the requirements of transfer or mechanical/thermal impedance matching,when the input and output port given specific materials,the configuration materials distribution of compliant mechanisms obtained by topology optimization of the multi-material compliant mechanisms with geometrical nonlinearities can satisfy the material boundary conditions.(4)Topology optimization of multi-materials compliant mechanisms with geometrical nonlinearities considering stress constraines.Separable Stress Interpolation model was used to calculate the element stress of each phase material.The maximum of output displacement of compliant mechanisms is developed as the objective function;The volume fraction and the global stress of each phase material is developed as the constraint conditions;The topology optimization model of multi-materials compliant mechanisms with geometrical nonlinearities considering stress-constrained was established.Numerical examples verify the effectiveness of the proposed design method.The maximum stress of each phase material of compliant mechanisms is less than or equal to its permissible stress constraint value in topology configuration,which makes the mechanisms meet the strength failure,and effectively reduces the stress level and stress concentration.