Multiscale Topology Optimization of Periodic Structures Taking into Account Strain Gradient

2019 ◽  
pp. 29-55
Keyword(s):  
Topology Optimization ◽  
Strain Gradient ◽  
Periodic Structures

Dimension reduction and surrogate based topology optimization of periodic structures

2019 ◽  
Vol 229 ◽  
pp. 111385 ◽  
Author(s):  
Min Li ◽  
Zhibao Cheng ◽  
Gaofeng Jia ◽  
Zhifei Shi
Keyword(s):  
Topology Optimization ◽  
Dimension Reduction ◽  
Periodic Structures

Topology Optimization of Periodic Structures With Substructuring

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Junjian Fu ◽  
Liang Xia ◽  
Liang Gao ◽  
Mi Xiao ◽  
Hao Li
Keyword(s):  
Topology Optimization ◽  
Linear System ◽  
Periodic Structures ◽  
Computational Cost ◽  
Optimization Method ◽  
Displacement Fields ◽  
Element Analysis ◽  
Level Set Function ◽  
Static Condensation ◽  
Unit Cells

Topology optimization of macroperiodic structures is traditionally realized by imposing periodic constraints on the global structure, which needs to solve a fully linear system. Therefore, it usually requires a huge computational cost and massive storage requirements with the mesh refinement. This paper presents an efficient topology optimization method for periodic structures with substructuring such that a condensed linear system is to be solved. The macrostructure is identically partitioned into a number of scale-related substructures represented by the zero contour of a level set function (LSF). Only a representative substructure is optimized for the global periodic structures. To accelerate the finite element analysis (FEA) procedure of the periodic structures, static condensation is adopted for repeated common substructures. The macrostructure with reduced number of degree of freedoms (DOFs) is obtained by assembling all the condensed substructures together. Solving a fully linear system is divided into solving a condensed linear system and parallel recovery of substructural displacement fields. The design efficiency is therefore significantly improved. With this proposed method, people can design scale-related periodic structures with a sufficiently large number of unit cells. The structural performance at a specified scale can also be calculated without any approximations. What’s more, perfect connectivity between different optimized unit cells is guaranteed. Topology optimization of periodic, layerwise periodic, and graded layerwise periodic structures are investigated to verify the efficiency and effectiveness of the presented method.

scholarly journals Synthesis of Bistable Periodic Structures Using Topology Optimization and a Genetic Algorithm

2005 ◽  
Author(s):  
Jitendra Prasad ◽  
Alejandro Diaz
Keyword(s):  
Genetic Algorithm ◽  
Topology Optimization ◽  
Periodic Structures ◽  
Performance Criterion ◽  
Ground Structure ◽  
Structure Approach ◽  
Automatic Synthesis ◽  
Compliant Structure ◽  
Beam Elements ◽  
Ground Structure Approach

Formulations for the automatic synthesis of two-dimensional bistable, compliant periodic structures are presented, based on standard methods for topology optimization. The design space is parameterized using non-linear beam elements and a ground structure approach. A performance criterion is suggested, based on characteristics of the load-deformation curve of the compliant structure. A genetic algorithm is used to find candidate solutions. A numerical implementation of this methodology is discussed and illustrated using a simple example.

scholarly journals Periodic structures stiffness topology optimization

2019 ◽  
Author(s):  
Joao Victor Watanabe Nunes ◽  
Renato Pavanello
Keyword(s):  
Topology Optimization ◽  
Boundary Conditions ◽  
Periodic Structures ◽  
Computational Costs ◽  
Evolutionary Structural Optimization ◽  
Low Weight ◽  
Uniform Medium ◽  
Refined Meshes ◽  
Optimum Topology ◽  
Periodic Materials

Stiffness topology optimization aims to determine the best material arrangement, capable of conciliating high structural stiffness and low weight, which handles certain loading conditions subjected to predefined boundary conditions. The imposed periodic constrain is fundamented on the fact that structures made of periodic materials behave as a homogeneous continuum, because the macro-structure cells are modeled as a uniform medium composed by periodic material. The optimization algorithm used in this work is the BESO (Bi-directional Evolutionary Structural Optimization), which analyzes the structure, under its loadings and boundary conditions, and generates the optimum topology through addition and removal of material. However, in order to reduce the high computational costs of this method when applied to very refined meshes, which is the case with most periodic structures, emphasis was placed on the integration between Matlab and Ansys softwares, with promising results.

scholarly journals Homogenization of frame lattices leading to second gradient models coupling classical strain and strain-gradient terms

2019 ◽  
Vol 24 (12) ◽  
pp. 3976-3999 ◽  
Author(s):  
Houssam Abdoul-Anziz ◽  
Pierre Seppecher ◽  
Cédric Bellis
Keyword(s):  
Displacement Field ◽  
Strain Gradient ◽  
Periodic Structures ◽  
Three Dimensional ◽  
Discrete Systems ◽  
Effective Energy ◽  
Classical Strain ◽  
Second Gradient ◽  
Second Gradient Models ◽  
Gradient Models

We determine in the framework of static linear elasticity the homogenized behavior of three-dimensional periodic structures made of welded elastic bars. It has been shown that such structures can be modeled as discrete systems of nodes linked by extensional, flexural/torsional interactions corresponding to frame lattices and that the corresponding homogenized models can be strain-gradient models, i.e., models whose effective elastic energy involves components of the first and the second gradients of the displacement field. However, in the existing models, there is no coupling between the classical strain and the strain-gradient terms in the expression of the effective energy. In the present article, under some assumptions on the positions of the nodes of the unit cell, we show that classical strain and strain-gradient strain terms can be coupled. In order to illustrate this coupling we compute the homogenized energy of a particular structure that we call asymmetrical pantographic structure.

Sign in / Sign up

Export Citation Format

Share Document