Topology Optimization With Multiple Displacement Equality Constraints And Application

The orthogonality between the axes of the photoelectric theodolite have an important influence on the accuracy of the aiming measurement of the equipment.With the development of the modernization of the shooting range,further light weighting requirements for optoelectronic precision measuring equipment are proposed.This means it needs improvement of stiffness redundancy in traditional structural design.Lightweight design and ensuring orthogonality between horizontal and vertical axis systems in the equipment has proposed via the displacement constraint problem in optimization.In order to satisfy the need for equal structural displacement in the light weight design of support structures in fine optoelectronic tracking devices.Based on the variable density SIMP method,this paper studies the topology optimization method with multi-point displacement equality constraints.The problem of displacement equality constraint at multiple arbitrary local nodes in topology optimization is solved.Implement of light weight design with displacement constraint for key components of photoelectric theodolite.The main work of this paper is as follows:An augmented Lagrangian multiplier method based on reaction force is proposed.Considering the nature physical meaning of the Lagrangian multiplier,which is the reaction force in the node that apply the displacement constraint in the finite element theory of variational principle of mechanical problems,the reaction force is used to approximately replace the Lagrangian multiplier in the equality constraint optimization problem.In the traditional simple mathematical optimization method,the multiplier need to be solved multiple times to approach the true value.This method can effectively reduce the number of cycles and solve multiple constraints just with solving a positive problem for one time.A structural topology optimization model is proposed which based on the SIMP method with maximum stiffness as objective while having the constraints of volume and equal displacement.The displacement equality constraints were introduced to the original objective function through the augmented Lagrangian multiplier method.When solving the Lagrangian multiplier,an approximate substitution method was used which considers its corresponding real physical meaning instead of the traditional pure mathematical iterative approximation method.By using the adjoint method,the augmented objective function sensitivity was obtained.By applying the MMA optimization algorithm,the design variables are updated while satisfying the volumetric constraint.Finally,numerical examples were presented to illustrate the effectiveness of the method in designing lightweight structure with maximum stiffness and multiple displacement constraints.Verification of displacement constrained topology optimization results using mechanical displacement measurement experiments.According to the directly irradiation laser triangulation principle,the laser displacement sensor is used to measure the displacement of MBB beam structure in the same load condition which applied in the original optimization of MBB beam.The MBB beam is manufactured by light curing rapid prototyping additive manufacturing method.The effect of the displacement constraint is verified by calculating the displacement ratio of the optimized design constraint point.Research on displacement constrained topology optimization of key components of photoelectric theodolite tracking frame.Optimization of the theodolite tracking frame based on the proposed multi-point displacement equality constrained topology optimization method is accomplished by using the second development of the FEM numerical calculation software COMSOL Multiphysics.Displacement constrained optimization of static stiffness maximal structure provides reference to the light weight design of the turntable for static performance enhancement.