A Moving Morphable Component Based Topology Optimization Approach for Rib-Stiffened Structures Considering Buckling Constraints

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Weisheng Zhang ◽  
Ying Liu ◽  
Zongliang Du ◽  
Yichao Zhu ◽  
Xu Guo
Keyword(s):  
Topology Optimization ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Base Plate ◽  
Optimization Approach ◽  
Element Analysis ◽  
Buckling Constraints ◽  
Design Variables ◽  
Stiffened Structures ◽  
Stiffening Ribs

Stiffened structures are widely used in industry. However, how to optimally distribute the stiffening ribs on a given base plate remains a challenging issue, partially because the topology and geometry of stiffening ribs are often represented in a geometrically implicit way in traditional approaches. This implicit treatment may lead to problems such as high computational cost (caused by the large number of design variables, geometry constraints in optimization, and large degrees-of-freedom (DOF) in finite element analysis (FEA)) and the issue of manufacturability. This paper presents a moving morphable component (MMC)-based approach for topology optimization of rib-stiffened structures, where the topology and the geometry of stiffening ribs are explicitly described. The proposed approach displays several prominent advantages, such as (1) both the numbers of design variables and DOF in FEA are reduced substantially; (2) the proper manufacture-related geometry requirements of stiffening ribs can be readily satisfied without introducing any additional constraint. The effectiveness of the proposed approach is further demonstrated with numerical examples on topology optimization of rib-stiffened structures with buckling constraints.

Dynamic Optimization of Steel Catenary Risers Based on Reliability Using Metamodel

2010 ◽  
Author(s):  
Wenqing Zheng ◽  
Hezhen Yang
Keyword(s):  
Dynamic Optimization ◽  
Computational Cost ◽  
Minimum Cost ◽  
Probabilistic Constraints ◽  
Optimization Approach ◽  
Element Analysis ◽  
Steel Catenary Riser ◽  
Reliability Based Design ◽  
Minimum Cost Design ◽  
Steel Catenary Risers

Reliability based design optimization (RBDO) of a steel catenary riser (SCR) using metamodel is investigated. The purpose of the optimization is to find the minimum-cost design subjecting to probabilistic constraints. To reduce the computational cost of the traditional double-loop RBDO, a single-loop RBDO approach is employed. The performance function is approximated by using metamodel to avoid time consuming finite element analysis during the dynamic optimization. The metamodel is constructed though design of experiments (DOE) sampling. In addition, the reliability assessment is carried out by Monte Carlo simulations. The result shows that the RBDO of SCR is a more rational optimization approach compared with traditional deterministic optimization, and using metamodel technique during the dynamic optimization process can significantly decrease the computational expense without sacrificing accuracy.

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.

Structural Dynamic Topology Optimization of the Transmission Housing

2011 ◽  
Vol 308-310 ◽  
pp. 368-372
Author(s):  
Shou Wen Yao ◽  
Jian Li Lv ◽  
Qing Dong Peng
Keyword(s):  
Topology Optimization ◽  
Dynamic Performance ◽  
Cad Model ◽  
Mass Reduction ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Design Variables ◽  
The Finite Element Analysis ◽  
Dynamic Topology ◽  
Topology Model

Dynamic performance is one of the most important factors in the product’s life. Transmission housing is one of the important components in vehicle, which has direct influence on the vehicle’s powertrain performance. Dynamic topology optimization can improve the product’s performance. The dynamic topology model is built, in which the density of elements are the design variables, the displacement of frequency response and volume are the constraints, and the objective is to maximize the first natural frequency of the housing. According to the result of optimization, the CAD model of housing is rebuilt and the finite element analysis of the new housing is done.The results show that both the static and dynamic performance are improved besides the mass reduction, namely, dynamic topology optimization can significantly improve the product’s performance.

Application of Regional Strain Energy in Topology Optimization With Inertia Relief Analysis

2013 ◽  
Author(s):  
Wei Song ◽  
Hae Chang Gea ◽  
Ren-Jye Yang ◽  
Ching-Hung Chuang
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Strain Energy ◽  
Computational Cost ◽  
Structure Design ◽  
Protective Structure ◽  
Element Analysis ◽  
Regional Strain ◽  
Unbalanced Loads ◽  
Energy Formulation

In finite element analysis, inertia relief solves the response of an unconstrained structure subject to constant or slowly varying external loads with static analysis computational cost. It is very attractive to utilize it in topology optimization to design structures under unbalanced loads, such as in impact and drop phenomena. In this paper, regional strain energy formulation and inertia relief is integrated into topology optimization to design protective structure under unbalanced loads. For background, the equations of inertia relief are introduced and a commonly used solving method is revisited. Then the regional strain energy formulation for topology optimization with inertia relief is proposed and its sensitivity is derived from the adjoint method. Based on the solving method, the sensitivity is evaluated term by term to simplify the results. The simplified sensitivity can be calculated easily using the output of commercial finite element packages. Finally, the effectiveness of this formulation is shown in the first example and the proposed regional strain energy formulation for topology optimization with inertia relief are presented and discussed in the protective structure design examples.

scholarly journals Gradient-based topology optimization of soft dielectrics as tunable phononic crystals

2021 ◽  
Author(s):  
Atul Kumar Sharma ◽  
Gal Shmuel ◽  
Oded Amir
Keyword(s):  
Topology Optimization ◽  
Electric Fields ◽  
Computational Cost ◽  
Optimization Method ◽  
Phononic Crystals ◽  
Frequency Bands ◽  
Design Variables ◽  
Gradient Based ◽  
Soft Dielectrics ◽  
Design Freedom

Dielectric elastomers are active materials that undergo large deformations and change their instantaneous moduli when they are actuated by electric fields. By virtue of these features, composites made of soft dielectrics can filter waves across frequency bands that are electrostatically tunable. To date, to improve the performance of these adaptive phononic crystals, such as the width of these bands at the actuated state, metaheuristics-based topology optimization was used. However, the design freedom offered by this approach is limited because the number of function evaluations increases exponentially with the number of design variables. Here, we go beyond the limitations of this approach, by developing an efficient gradient-based topology optimization method. The numerical results of the method developed here demonstrate prohibited frequency bands that are indeed wider than those obtained from the previous metaheuristics-based method, while the computational cost to identify them is reduced by orders of magnitude.

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.

A MultiDisciplinary Optimization Approach for Sizing Vertical Lift Aircraft

2021 ◽  
Author(s):  
Ananth Sridharan ◽  
Bharath Govindarajan
Keyword(s):  
Optimal Solution ◽  
Multidisciplinary Optimization ◽  
Shape Design ◽  
Optimization Approach ◽  
Optimization Strategy ◽  
Clock Time ◽  
Element Analysis ◽  
Analysis And Design ◽  
Design Variables ◽  
Vertical Lift

This paper presents an approach to reframe the sizing problem for vertical-lift unmanned aerial vehicles (UAVs) as an optimization problem and obtains a weight-optimal solution with up to two orders of magnitude of savings in wall clock time. Because sizing is performed with higher fidelity models and design variables from several disciplines, the Simultaneous Analysis aNd Design (SAND) approach from fixed-wing multidisciplinary optimization literature is adapted for the UAV sizing task. Governing equations and disciplinary design variables that are usually self-contained within disciplines (airframe tube sizes, trim variables, and trim equations) are migrated to the sizing optimizer and added as design variables and (in)equality constraints. For sizing consistency, the iterative weight convergence loop is replaced by a coupling variable and associated equality consistency constraint for the sizing optimizer. Cruise airspeed is also added as a design variable and driven by the sizing optimizer. The methodology is demonstrated for sizing a package delivery vehicle (a lift-augment quadrotor biplane tailsitter) with up to 39 design variables and 201 constraints. Gradient-based optimizations were initiated from different starting points; without blade shape design in sizing, all processes converged to the same minimum, indicating that the design space is convex for the chosen bounds, constraints, and objective function. Several optimization schemes were investigated by moving combinations of relevant disciplines (airframe sizing with finite element analysis, vehicle trim, and blade aerodynamic shape design) to the sizing optimizer. The biggest advantage of the SAND strategy is its scope for parallelization, and the inherent ability to drive the design away from regions where disciplinary analyses (e.g., trim) cannot find a solution, obviating the need for ad hoc penalty functions. Even in serial mode, the SAND optimization strategy yields results in the shortest wall clock time compared to all other approaches.

scholarly journals Multidisciplinary Optimisation of Aircraft Structures with Critical Non-Regular Areas: Current Practice and Challenges

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 223
Author(s):  
Massimo Sferza ◽  
Jelena Ninić ◽  
Dimitrios Chronopoulos ◽  
Florian Glock ◽  
Fernass Daoud
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Aircraft Design ◽  
Element Model ◽  
Main Role ◽  
Design Optimisation ◽  
Load Paths ◽  
Design Variables ◽  
Internal Deformation ◽  
Multidisciplinary Design Optimisation

The design optimisation of aerostructures is largely based on Multidisciplinary Design Optimisation (MDO), which is a set of tools used by the aircraft industry to size primary structures: wings, large portions of the fuselage or even an entire aircraft. The procedure is computationally expensive, as it must account for several thousands of loadcases, multiple analyses with hundreds of thousands of degrees of freedom, thousands of design variables and millions of constraints. Because of this, the coarse Global Finite Element Model (GFEM), on which the procedure is based, cannot be further refined. The structures represented in the GFEM contain many components and non-regular areas, which require a detailed modelling to capture their complex mechanical behaviour. Instead, in the GFEM, these components are represented by simplified models with approximated stiffness, whose main role is to contribute to the identification of the load paths over the whole structure. Therefore, these parts are kept fixed and are not constrained during the optimisation, as the description of their internal deformation is not sufficiently accurate. In this paper, we show that it would nevertheless be desirable to size the non-regular areas and the overall structures at once. Firstly, we introduce the concept of non-regular areas in the context of a structural airframe MDO. Secondly, we present a literature survey on MDO with a critical review of several architectures and their current applications to aircraft design optimisation. Then, we analyse and demonstrate with examples the possible consequences of neglecting non-regular areas when MDO is applied. In the conclusion, we analyse the requirements for alternative approaches and why the current ones are not viable solutions. Lastly, we discuss which characteristics of the problem could be exploited to contain the computational cost.

scholarly journals An explicit topology optimization method using moving polygonal morphable voids (MPMVs)

2020 ◽  
Vol 23 (2) ◽  
pp. 536-540 ◽  
Author(s):  
Hoang Van-Nam
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Optimization Method ◽  
Density Field ◽  
Optimization Approach ◽  
Design Variables ◽  
Mesh Independence ◽  
Gradient Based ◽  
Element Density ◽  
Optimization Solvers

Introduction: Conventional topology optimization approaches are implemented in an implicit manner with a very large number of design variables, requiring large storage and computation costs. In this study, an explicit topology optimization approach is proposed by movonal morphable voids whose geometry parameters are considered as design variables. Methods: Each polygonal void plays as an empty-material zone that can move, change its shapes, and overlap with its neighbors in a design space. The geometry eters of MPMVs consisting of the coordinates of polygonal vertices are utilized to render the structure in the design domain in an element density field. The density function of the elements located inside polygonal voids is described by a smooth exponential function that allows utilizing gradient-based optimization solvers. Results & Conclusion: Compared with conventional topology optimization approaches, the MPMV approach uses fewer design variables, ensure mesh-independence solution without filtering techniques or perimeter constraints. Several numerical examples are solved to validate the efficiency of the MPMV approach.

scholarly journals Self-Directed Online Machine Learning for Topology Optimization

2021 ◽  
Author(s):  
Changyu Deng ◽  
Yizhou Wang ◽  
Can Qin ◽  
Wei Lu
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Computational Cost ◽  
Region Of Interest ◽  
Global Optimum ◽  
Training Data ◽  
Computational Time ◽  
Minimization Problems ◽  
Design Variables

Abstract Topology optimization by optimally distributing materials in a given domain requires gradient-free optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report a Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNN's prediction of the global optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. Our algorithm was tested by compliance minimization problems and fluid-structure optimization problems. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.

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