Non-Probabilistic Based Topology Optimization Under External Load Uncertainty With Eigenvalue-Superposition of Convex Models

2013 ◽  
Author(s):  
Xike Zhao ◽  
Hae Chang Gea ◽  
Wei Song
Keyword(s):  
Topology Optimization ◽  
External Load ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Convex Model ◽  
Structure Response ◽  
Gradient Based ◽  
Bounded Convex ◽  
Topology Optimization Method

In this paper the Eigenvalue-Superposition of Convex Models (ESCM) based topology optimization method for solving topology optimization problems under external load uncertainties is presented. The load uncertainties are formulated using the non-probabilistic based unknown-but-bounded convex model. The sensitivities are derived and the problem is solved using gradient based algorithm. The proposed ESCM based method yields the material distribution which would optimize the worst structure response under the uncertain loads. Comparing to the deterministic based topology optimization formulation the ESCM based method provided more reasonable solutions when load uncertainties were involved. The simplicity, efficiency and versatility of the proposed ESCM based topology optimization method can be considered as a supplement to the sophisticated reliability based topology optimization methods.

scholarly journals An Efficient and High-Resolution Topology Optimization Method Based on Convolutional Neural Networks

2019 ◽  
Author(s):  
Liang Xue ◽  
Jie Liu ◽  
Guilin Wen ◽  
Hongxin Wang
Keyword(s):  
Topology Optimization ◽  
High Resolution ◽  
High Efficiency ◽  
Optimization Problems ◽  
Combined Treatment ◽  
Computational Cost ◽  
Optimization Method ◽  
Element Analysis ◽  
Arbitrary Boundary ◽  
Topology Optimization Method

Topology optimization is a pioneering design method that can provide various candidates with high mechanical properties. However, the high-resolution for the optimum structures is highly desired, normally in turn leading to computationally intractable puzzle, especially for the famous Solid Isotropic Material with Penalization (SIMP) method. In this paper, an efficient and high-resolution topology optimization method is proposed based on the Super-Resolution Convolutional Neural Network (SRCNN) technique in the framework of SIMP. The SRCNN includes four processes, i.e. refining, path extraction & representation, non-linear mapping, and reconstruction. The high computational efficiency is achieved by a pooling strategy, which can balance the number of finite element analysis (FEA) and the output mesh in optimization process. To further reduce the high computational cost of 3D topology optimization problems, a combined treatment method using 2D SRCNN is built as another speeding-up strategy. A number of typical examples justify that the high-resolution topology optimization method adopting SRCNN has excellent applicability and high efficiency for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.

Buckling Topology Optimization of Laminated Multi-Material Composite Structures

2006 ◽  
Author(s):  
Erik Lund
Keyword(s):  
Topology Optimization ◽  
Composite Structures ◽  
Optimization Problems ◽  
Combinatorial Problem ◽  
Optimization Method ◽  
Load Factor ◽  
Material Optimization ◽  
Material Stiffness ◽  
Gradient Based ◽  
Material Composite

The design problem of maximizing the buckling load factor of laminated multi-material composite shell structures is investigated using the so-called Discrete Material Optimization (DMO) approach. The design optimization method is based on ideas from multi-phase topology optimization where the material stiffness is computed as a weighted sum of candidate materials, thus making it possible to solve discrete optimization problems using gradient based techniques and mathematical programming. The potential of the DMO method to solve the combinatorial problem of proper choice of material and fiber orientation simultaneously is illustrated for a multilayered plate example and a simplified shell model of a spar cap of a wind turbine blade.

scholarly journals Experimental Observation of the Skeletal Adaptive Repair Mechanism and Bionic Topology Optimization Method

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Kaysar Rahman ◽  
Mamtimin Geni ◽  
Mamatjan Mamut ◽  
Nijat Yusup ◽  
Muhtar Yusup
Keyword(s):  
Topology Optimization ◽  
Bone Remodeling ◽  
External Load ◽  
Optimization Problems ◽  
Reaction Diffusion ◽  
Optimization Method ◽  
Experimental Result ◽  
Spongy Bone ◽  
Ct Data ◽  
Cross Type

Bone adaptive repair theory considers that the external load is the direct source of bone remodeling; bone achieves its maintenance by remodeling some microscopic damages due to external load during the process. This paper firstly observes CT data from the whole self-repairing process in bone defects in rabbit femur. Experimental result shows that during self-repairing process there exists an interaction relationship between spongy bone and enamel bone volume changes of bone defect, that is when volume of spongy bone increases, enamel bone decreases, and when volume of spongy bone decreases, enamel bone increases. Secondly according to this feature a bone remodeling model based on cross-type reaction-diffusion system influenced by mechanical stress is proposed. Finally, this model coupled with finite element method by using the element adding and removing process is used to simulate the self-repairing process and engineering optimization problems by considering the idea of bionic topology optimization.

scholarly journals Efficient, high-resolution topology optimization method based on convolutional neural networks

2021 ◽  
Author(s):  
Liang Xue ◽  
Jie Liu ◽  
Guilin Wen ◽  
Hongxin Wang
Keyword(s):  
Topology Optimization ◽  
High Resolution ◽  
High Efficiency ◽  
Optimization Problems ◽  
Combined Treatment ◽  
Computational Cost ◽  
Treatment Method ◽  
Optimization Method ◽  
Arbitrary Boundary ◽  
Topology Optimization Method

AbstractTopology optimization is a pioneer design method that can provide various candidates with high mechanical properties. However, high resolution is desired for optimum structures, but it normally leads to a computationally intractable puzzle, especially for the solid isotropic material with penalization (SIMP) method. In this study, an efficient, high-resolution topology optimization method is developed based on the superresolution convolutional neural network (SRCNN) technique in the framework of SIMP. SRCNN involves four processes, namely, refinement, path extraction and representation, nonlinear mapping, and image reconstruction. High computational efficiency is achieved with a pooling strategy that can balance the number of finite element analyses and the output mesh in the optimization process. A combined treatment method that uses 2D SRCNN is built as another speed-up strategy to reduce the high computational cost and memory requirements for 3D topology optimization problems. Typical examples show that the high-resolution topology optimization method using SRCNN demonstrates excellent applicability and high efficiency when used for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.

Topology Optimization of Planar Gear-Linkage Mechanisms

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Neung Hwan Yim ◽  
Seok Won Kang ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Optimization Method ◽  
Mechanism Synthesis ◽  
Gear Design ◽  
Linkage Design ◽  
Gradient Based ◽  
Mechanical Elements ◽  
Topology Optimization Method

Topology optimization for mechanism synthesis has been developed for the simultaneous determination of the number and dimension of mechanisms. However, these methods can be used to synthesize linkage mechanisms that consist only of links and joints because other types of mechanical elements such as gears cannot be simultaneously synthesized. In this study, we aim to develop a gradient-based topology optimization method which can be used to synthesize mechanisms consisting of both linkages and gears. For the synthesis, we propose a new ground model defined by two superposed design spaces: the linkage and gear design spaces. The gear design space is discretized by newly proposed gear blocks, each of which is assumed to rotate as an output gear, while the linkage design space is discretized by zero-length-spring-connected rigid blocks. Another set of zero-length springs is introduced to connect gear blocks to rigid blocks, and their stiffness values are varied to determine the existence of gears when they are necessary to produce the desired path. After the proposed topology-optimization-based synthesis formulation and its numerical implementation are presented, its effectiveness and validity are checked with various synthesis examples involving gear-linkage and linkage-only mechanisms.

Topology Optimization With Unknown-but-Bounded Load Uncertainty

2014 ◽  
Author(s):  
Xike Zhao ◽  
Wei Song ◽  
Hae Chang Gea ◽  
Limei Xu
Keyword(s):  
Topology Optimization ◽  
Strain Energy ◽  
Optimization Problem ◽  
Solution Procedure ◽  
Convex Model ◽  
Load Uncertainty ◽  
Topology Optimization Problem ◽  
Structure Response ◽  
Gradient Based ◽  
Upper Level

In this paper, convex modeling based topology optimization with load uncertainty is presented. The load uncertainty is described using the non-probabilistic based unknown-but-bounded convex model, and the strain energy based topology optimization problem under uncertain loads is formulated. Unlike the conventional deterministic topology optimization problem, the maximum possible strain energy under uncertain loads is selected as the new objective in order to achieve a safe solution. Instead of obtaining approximated solutions as used before, an exact solution procedure is presented. The problem is first formulated as a single level optimization problem, and then rewritten as a two-level optimization problem. The upper level optimization problem is solved as a deterministic topology optimization with the load which generated from the worst structure response in the lower level problem. The lower level optimization problem is to identify this worst structure response, and it is found equivalent to an inhomogeneous eigenvalue problem. Three different cases are discussed for accurately evaluating the global optima of the lower level optimization problem, while the corresponding sensitivities are derived individually. With the function value and sensitivity information ready, the upper level optimization problem can be solved through existing gradient based optimization algorithms. The effectiveness of the proposed convex modeling based topology optimization is demonstrated through different numerical examples.

Synthesis of Gear-Linkage Mechanisms by Topology Optimization

2018 ◽  
Author(s):  
Neung Hwan Yim ◽  
Seok Won Kang ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Synthesis Method ◽  
Variable Stiffness ◽  
Optimization Methods ◽  
Optimization Method ◽  
Planar Mechanisms ◽  
Gear Design ◽  
Linkage Design ◽  
Gradient Based

This work is concerned with a new mechanism synthesis method for the simultaneous determination of the type, number and dimension of mechanisms by topology optimization. Earlier topology optimization methods can synthesize linkage mechanisms that consist only of links and joints. The proposed synthesis method is a gradient-based topology optimization method useful for the synthesis of planar mechanisms consisting of linkages and gears. To formulate the topology optimization based method, we propose two superposed design spaces as a ground structure: the linkage and gear design spaces. The gear design space is discretized by newly proposed gear blocks while the linkage design space by rigid blocks. The zero-length springs with variable stiffness are used to control the connectivity of blocks, which in turns determines the configuration of the synthesized mechanism. After the proposed topology-optimization-based synthesis formulation is presented, its effectiveness and validity are checked with various synthesis examples.

scholarly journals Topology Optimization of Hard-Coating Thin Plate for Maximizing Modal Loss Factors

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 774
Author(s):  
Haitao Luo ◽  
Rong Chen ◽  
Siwei Guo ◽  
Jia Fu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Composite Plates ◽  
Optimization Method ◽  
Hard Coating ◽  
Design Variables ◽  
Coating Composite ◽  
Damping Materials ◽  
Topology Optimization Method ◽  
Loss Factors

At present, hard coating structures are widely studied as a new passive damping method. Generally, the hard coating material is completely covered on the surface of the thin-walled structure, but the local coverage cannot only achieve better vibration reduction effect, but also save the material and processing costs. In this paper, a topology optimization method for hard coated composite plates is proposed to maximize the modal loss factors. The finite element dynamic model of hard coating composite plate is established. The topology optimization model is established with the energy ratio of hard coating layer to base layer as the objective function and the amount of damping material as the constraint condition. The sensitivity expression of the objective function to the design variables is derived, and the iteration of the design variables is realized by the Method of Moving Asymptote (MMA). Several numerical examples are provided to demonstrate that this method can obtain the optimal layout of damping materials for hard coating composite plates. The results show that the damping materials are mainly distributed in the area where the stored modal strain energy is large, which is consistent with the traditional design method. Finally, based on the numerical results, the experimental study of local hard coating composites plate is carried out. The results show that the topology optimization method can significantly reduce the frequency response amplitude while reducing the amount of damping materials, which shows the feasibility and effectiveness of the method.

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