Fatigue Topology Optimization Design Based on Distortion Energy Theory and Independent Continuous Mapping Method

Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.

ICM Method Combined with Meshfree Approximation for Continuum Structure

The independent continuous mapping（ICM） method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented.To facilitate the enforcement of the essential boundary condition and derivative of various sensitivities,a singular weight function in element free Galerkin method is introduced.Material point variable is defined to illustrate the condition of material point and its vicinity instead of element or node.The topological variables field is constructed by moving least square approximation which inherits the continuity and smoothness of the weight function.Due to reciprocal relationships between the topological variables and design variables,various structural responses sensitivities are derived according to the method for calculating the partial derivatives of compound functions.Numerical examples indicate that checkerboard pattern and mesh-dependence phenomena are overcome without additional restriction methods.

Concurrent topology optimization for minimization of total mass considering load-carrying capabilities and thermal insulation simultaneously

The present work introduces a novel concurrent optimization formulation to meet the requirements of lightweight design and various constraints simultaneously.Nodal displacement of macrostructure and effective thermal conductivity of microstructure are regarded as the constraint functions, which means taking into account both the loadcarrying capabilities and the thermal insulation properties.The effective properties of porous material derived from numerical homogenization are used for macrostructural analysis. Meanwhile, displacement vectors of macrostructures from original and adjoint load cases are used for sensitivity analysis of the microstructure. Design variables in the form of reciprocal functions of relative densities are introduced and used for linearization of the constraint function. The objective function of total mass is approximately expressed by the second order Taylor series expansion. Then, the proposed concurrent optimization problem is solved using a sequential quadratic programming algorithm, by splitting into a series of sub-problems in the form of the quadratic program. Finally, several numerical examples are presented to validate the effectiveness of the proposed optimization method. The various effects including initial designs, prescribed limits of nodal displacement, and effective thermal conductivity on optimized designs are also investigated. An amount of optimized macrostructures and their corresponding microstructures are achieved.

Fail-safe topology optimization of continuum structures with fundamental frequency constraints based on the ICM method

It is an important topic to improve the redundancy of optimized configuration to resist the local failure in topology optimization of continuum structures.Such a fail-safe topology optimization problem has been solved effectively in the ficld of statics.In this paper,the fail-safe topology optimization problem is extended to the field of frequency topology optimization.Based on the independent continuous mapping(ICM)method,the model of fail-safe topology optimization is established with the objective of minimal weight integrating with the discrete condition of topological variables and the constraint of the fundamental frequency.The fail-safe optimization model established above is substituted by a sequence of subproblems in the form of the quadratic program with exact second-order information and solved efficiently by the dual sequence quadratic programming(DSQP)algorithm.The numerical result reveals that the optimized fail-safe structure has more complex configuration and preserved materials than the structure obtained from the traditional frequency topology optimization,which means that the optimized fail-safe structure has higher redundancy.Moreover,the optimized fail-safe structure guarantees that the natural frequency meets the constraint of fundamental frequency when the local failure ocurs,which can avoid the structural frequency to be sensitive to local failure.The fail-safe optimirzation topology model is proved effective and feasible by four numerical examples.