A novel multi-resolution scheme to perform the multi-material topology optimization in the framework of isogeometric analysis (IGA) is proposed. To create high resolution optimized designs with a ...lower computational cost, a new variable parameter space is supplemented to define design density variables and represent the optimal material distribution utilizing the bivariate B-spline basis functions. These functions are simply obtained by k-refinement strategy in the IGA. The non-uniform rational B-spline (NURBS) basis functions are employed to exactly describe geometric domains and approximate unknown solutions in finite element analysis (FEA) as well. An alternating active-phase algorithm associated with the block Gauss–Seidel method is employed to convert a multiphase topology optimization problem under multiple volume fraction constraints into many binary phase topology optimization sub-problems with only one volume fraction constraint. Accordingly, the number of design variables depends only on one active phase in each of those sub-problems regardless of the number of material phases and is significantly decreased in comparison with the original problem. The Optimality Criteria (OC) method is used as an optimizer to update solutions for such sub-problems. The effectiveness and robustness of the proposed method are verified via testing various benchmark examples.
•A novel multi-material multi-resolution topology optimization (MTOP) scheme using isogeometric analysis (IGA) is proposed.•A new variable parameter space is added to perform IGA-based MTOP.•The proposed method associated with the alternating active-phase algorithm is presented first.•Several benchmark problems are tested for validation of the present method.
This article firstly presents a novel numerical methodology to concurrently optimize material distribution (size) and thickness variation (shape) of multidirectional functionally graded (MFG) plates ...under free vibration within the isogeometric analysis (IGA) framework. An isogeometric multimesh design (IMD) approach is proposed to generate two distinct non-uniform rational B-spline (NURBS) surfaces via the k-refinement strategy. A finer analysis one relied upon a combination of the IGA and a generalized shear deformation theory (GSDT) is utilized for the unknown solution approximation in finite element analyses (FEAs). Whilst the other coarser design one is employed for the exact geometry representation as well as the optimal material and thickness depiction. Size and shape design variables are in turn the ceramic volume fraction and z-axis coordinate of the top side of the MFG plate coincidentally assigned to each of control points on this surface. Flexibly utilizing such two surfaces helps diminish a large number of design variables and considerably save the computational cost in optimization problems, yet still appropriately manifesting optimal material and thickness profiles. Additionally, this definition accurately simulates mechanical behavior of MFG plates in analysis ones as well. A recently developed derivative-free adaptive hybrid evolutionary firefly algorithm (AHEFA) is used to solve constrained frequency maximization problems. Several numerical examples are executed to verify the effectiveness and robustness of the present paradigm.
•A novel IMD approach for size and shape optimization of MFG plates is introduced.•Two separately defined NURBS surfaces are proposed for optimization and analyses.•The adaptive hybrid evolutionary firefly algorithm is utilized as an optimizer.•Several numerical examples are exhibited for the validation of the present paradigm.
Summary
The paper introduces a novel multiresolution scheme to topology optimization in the framework of the isogeometric analysis. A new variable parameter space is added to implement ...multiresolution topology optimization based on the Solid Isotropic Material with Penalization approach. Design density variables defined in the variable space are used to approximate the element analysis density by the bivariate B‐spline basis functions, which are easily obtained using k‐refinement strategy in the isogeometric analysis. While the nonuniform rational B‐spline basis functions are used to exactly describe geometric domains and approximate unknown solutions in finite element analysis. By applying a refined sensitivity filter, optimized designs include highly discrete solutions in terms of solid and void materials without using any black and white projection filters. The Method of Moving Asymptotes is used to solve the optimization problem. Various benchmark test problems including plane stress, compliant mechanism inverter, and 2‐dimensional heat conduction are examined to demonstrate the effectiveness and robustness of the present method.
This article proposes a novel topology framework for simultaneously optimizing topology, size and shape of truss structures with multiple constraints under static, free vibration and transient ...responses for the first time. To achieve such a purpose, the topology pseudo-area variable of members is newly proposed discretely assigning to either
10
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3
or 1 to respectively represent the absence or presence of a member. This suggestion aims at not only evading the numerical instability due to the singularity of global stiffness matrix when solving equilibrium equations in finite element analyses but also saving the computational effort owing to the intact preserve of FE model structure. The objective function of this study is to minimize the structural weight. The cross-sectional area of truss members is taken discrete/continuous design variables into account, whilst nodal coordinates are treated as continuous ones. In addition, kinematic stability, displacement, stress, Euler buckling loading, natural frequency and transient behavior are dealt with as constraints. The derivative-free adaptive hybrid evolutionary firefly algorithm is utilized as an optimizer to resolve such optimization problems including mixed continuous-discrete variables. A large number of benchmark examples are tested to verify the validity of the presented paradigm. Obtained outcomes indicate that the present methodology is effective and robust in searching better high-quality optimal solutions against many existing algorithms in the literature.
Effectiveness of several currently popular topology optimization methods is closely related to the number of design variables consisted of discretized finite elements. Since the number of design ...variables is proportional to the number of finite element meshes, a very fine discretization needs more computational cost to carry out a finite element analysis and evaluate a compliance based objective function with the volume constraint. This paper presents a new computational method by using convolutional neural networks (CNNs) which can be substituted for the FEM process to calculate compliances. The robustness and adaptability of the proposed method are tested on a MBB (Messerschmitt-Bölkow-Blohm) beam and two cantilever beam problems. The designed CNN is trained on a 48 × 16 pixel resolution dataset taken from coarse meshes. The trained CNN can predict the information of image-based topologies composed of fine meshes. A graphics processing unit (GPU) is then used to accelerate the bulk-processing of data.
•A new surrogated model is proposed to predict compliance information for topology optimization.•The proposed method can eliminate the step of FEM and accelerate optimization processes.•The CNNs are then introduced to train neural networks by using coarse elements.•High resolution image can be predicted in the trained NNs by using resize interpolation methods.•A GPU is then used to accelerate the bulk-processing of data.
•A novel adaptive hybrid evolutionary firefly algorithm (AHEFA) for shape and size optimization of truss structures under multiple frequency constraints is proposed.•This algorithm is a hybridization ...of the differential evolution (DE) algorithm and the firefly algorithm (FA).•The AHEFA significantly improves the convergence rate and the solution accuracy.•Six numerical examples are examined for the validity of the present algorithm.
This paper presents a novel adaptive hybrid evolutionary firefly algorithm (AHEFA) for shape and size optimization of truss structures under multiple frequency constraints. This algorithm is a hybridization of the differential evolution (DE) algorithm and the firefly algorithm (FA). An automatically adapted parameter is utilized to select an appropriate mutation scheme for an effective trade-off between the global and local search abilities. An elitist technique is applied to the selection phase to choose the best individuals. Accordingly, the convergence rate is significantly improved with the high solution accuracy. Six numerical examples are examined for the validity of the present algorithm.
This article introduces a simple and effective adaptive surrogate model to structural reliability analysis using deep neural network (DNN). In this paradigm, initial design of experiments (DoEs) are ...randomly selected from a given Monte Carlo Simulation (MCS) population to build the global approximate model of performance function (PF). More important points on the boundary of limit state function (LSF) and their vicinities are subsequently added relied on the surrogate model to enhance its accuracy without any complex techniques. A threshold is proposed to switch from a globally predicting model to a locally one for the approximation of LSF by eradicating previously used unimportant and noise points. Accordingly, the surrogate model becomes more precise for the MCS-based failure probability assessment with only a small number of experiments. Six numerical examples with highly nonlinear properties, various distributions of random variables and multiple failure modes, namely three benchmark ones regarding explicit mathematical PFs and the others relating to finite element method (FEM)-programmed truss structures under free vibration, are examined to validate the present approach.
•A DNN-based adaptive surrogate model for structural reliability analysis is proposed.•The performance and limit state functions are evaluated by the surrogate model.•A threshold is suggested to switch from a globally predicting model to a locally one.•The paradigm estimates the failure probability with only a small number of samples.•Six examples are investigated to confirm the reliability of the current methodology.
In this paper, an efficient deep unsupervised learning (DUL)-based framework is proposed to directly perform the design optimization of truss structures under multiple constraints for the first time. ...Herein, the members’ cross-sectional areas are parameterized using a deep neural network (DNN) with the middle spatial coordinates of truss elements as input data. The parameters of the network, including weights and biases, are regarded as decision variables of the structural optimization problem, instead of the member’s cross-sectional areas as those of traditional optimization algorithms. A new loss function of the network model is constructed with the aim of minimizing the total structure weight so that all constraints of the optimization problem via unsupervised learning are satisfied. To achieve the optimal parameters, the proposed model is trained to minimize the loss function by a combination of the standard gradient optimizer and backpropagation algorithm. As soon as the learning process ends, the optimum weight of truss structures is indicated without utilizing any other time-consuming metaheuristic algorithms. Several illustrative examples are investigated to demonstrate the efficiency of the proposed framework in requiring much lower computational cost against other conventional methods, yet still providing high-quality optimal solutions.
In this article, a novel idea of utilizing a non-uniform rational B-spline (NURBS)-based material mesh independently defined with the analysis mesh to represent the material distribution is ...introduced to free vibration and buckling problems of in-plane bi-directional functionally graded (IBFG) plates. Two power-law material models with the symmetrical and asymmetrical volume fraction distribution are proposed as the first experiment. By applying the
refinement scheme, the
continuous condition at symmetrical interfaces of material profiles can be easily achieved, while material gradations are still guaranteed elsewhere due to the outstanding advantage of material NURBS basis functions in controlling continuity. Either the rule of mixture or the Mori-Tanaka scheme is then used to estimate effective material properties. The analysis mesh is constructed by generalized shear deformation theory (GSDT)-based isogeometric analysis (IGA) for exactly modeling geometrical domains and approximately solving unknown solutions in finite element analysis (FEA). Accordingly, the
continuous requirement of the Galerkin isogeometric finite element model is simply met owing to the possibility of flexibly fulfilling high-order derivatives and continuity of analysis NUBRS functions. Additionally, the present formulation is also completely free from shear correction factors, yet still considering shear deformation influences. Several numerical examples are presented to demonstrate the performance and effectiveness of the proposed method. The effects of material gradations, aspect ratios, and different boundary conditions on IBFG plate responses are examined in detail as well.
Celotno besedilo
Dostopno za:
BFBNIB, DOBA, GIS, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
In this article, a density-driven unified multi-material topology optimization framework is suggested for functionally graded (FG) structures under static and dynamic responses. For this, ...two-dimensional solid structures and plate-like structures with/without variable thickness are investigated as design domains using multiple in-plane bi-directional FG materials (IBFGMs). In the present approach, a generally refined interpolation scheme relying upon Solid Isotropic Material with Penalization is proposed to deal with equivalent properties of IBFGMs. This methodology’s topological design variables are totally independent of all material phases. Therefore, the present method can yield separate material phases at their contiguous boundaries without intermediate density materials. The assumption of mixed interpolation of tensorial components of the 4-node shell element is employed to analyze plate elements, aiming to tackle the shear-locking phenomenon encountered as the optimal plate thickness becomes thinner. The mesh-independence filter is utilized to suppress the checkerboard formation of the material distribution. The method of Moving Asymptotes is used as an optimizer to update design variables in the optimization process. Several numerical examples are presented to evaluate the efficiency and reliability of the current approach.
