Number Of Finite Element Analyses Research Articles

Robust topology optimization of truss-like continuum structures under uncertain loads based on cloud model

The traditional structural performance may be seriously degraded due to applied indeterministic cases. A novel framework for robust topology optimization of truss-like continuum considering uncertain loads is presented. The robust optimization formula is constructed as minimizing the weighted sum of expectancy and standard variance of structural compliance with volume constraints. In this framework, both the magnitude and direction of applied loads are uncertain and independent. Truss-like continuum provides the topology optimal structure theoretically. Based on the classic truss-like optimization method, the statistical moments of compliance are accurately evaluated utilizing a bivariate cloud model tool. An effective strategy based on linear decoupling is reported to largely reduce the total number of finite element analysis. The optimization is achieved with gradient-based mathematic programming. Several numerical examples demonstrate a better structural robust performance obtained by the proposed algorithm than the traditional one.

An efficient approach for evaluating the reliability of engineering structures using support vector machine with clustering algorithm

ABSTRACT An implicit limit state function is predicted with a support vector machine (SVM) for reliability analysis of engineering structures to reduce the number of finite element analyses. The accuracy and predictability of the SVM method are reduced considerably by noise in data. In this paper, density-based spatial clustering of applications with noise (DBSCAN) is applied to reduce the noise in training samples for SVM regression. Then, the SVM model is linked with Monte Carlo simulation (MCS) to find out the reliability of the engineering structures. Four different examples of static and dynamic problems are solved to show acceptability and efficiency of the proposed method. It is observed that the proposed method is suitable for a smaller number of performance function calls. Direct MCS, artificial neural network-based MCS and response surface methods have been used to examine the effectiveness of the algorithm.

A deep reinforcement learning method for structural dominant failure modes searching based on self-play strategy

In the research area of structural reliability analysis (SRA), the dominant failure modes (DFMs) of a structural system make significant contributions to life-span failure prediction and safety assessment. However, the high computational cost caused by the combinatorial explosion is the main problem in DFMs searching that hinders its application and further development. Recently, many successful applications have proved that the self-play deep reinforcement learning (DRL) has a strong ability to obtain action policy in the face of combinatorial explosion problems. Inspired by this, a self-play strategy is designed to optimize the DRL-based DFMs searching process and reduce the computational effort. A scoring function is designed and used as the refereeing standard of the self-play games and helps improve the efficiency of Monte Carlo tree search (MCTS) in an asynchronous training process. In comparison with the β-unzipping method and exploration-based DFMs searching method, the proposed method significantly improved training efficiency with an accuracy of over 95% and a lower requirement of the number of finite element analysis (FEA), both of which contribute to the policy learning of failure component selection. In summary, the method shows potential applications for actual structures and makes valuable contributions to the problem with high computing costs.

A Numerical Twin Model for the Coupled Field Analysis of TEAM Workshop Problem 36

A numerical twin model for the magneto-thermal analysis of an induction heating device is proposed. The non-linearity of magnetic permeability against temperature – which characterizes the workpiece – is captured by the model, while the use of a Convolutional Neural Network (CNN), trained by a number of finite-element analyses, makes it possible to solve the following inverse problem: given a temperature map in the workpiece section, identify current and relevant frequency in the inductor coil, as well as the time instant at which the map refers to. The TEAM problem 36 is considered as the case study.

An efficient variable selection-based Kriging model method for the reliability analysis of slopes with spatially variable soils

The random finite element method (RFEM) is an efficient tool to demonstrate the spatial variability of soil properties during reliability analysis of slopes, but it requires remarkable model evaluations and computational efforts. In this paper, an efficient variable selection-based Kriging model method is proposed to approximate the finite element analysis model in reliability analysis of slopes. The variable selection technique successfully remedies the “curse of dimensionality” within Kriging model induced by the numerous random variables in random field discretization. The implementation procedure of this method for the reliability analysis of slopes is introduced in detail. Two typical examples of soil slopes, as well as a real complex slope are subsequently analyzed to illustrate the validity of the proposed method. The results show that the local loss of variability of random field due to the variable selection method has little impact on the safety factor of slopes. The proposed method can significantly reduce the number of finite element analysis and obtain accurate results in reliability analysis of slopes considering the spatial variability of soil properties.

Exact in-plane stress field solution for isotropic plates with circular holes reinforced with cylindrically orthotropic rings

In this paper an analytical solution for the stress distribution in an infinite plate with a concentrically reinforced hole under a general loading condition is derived. The developed solution explicitly accounts for the elastic properties of the plate and of the reinforcing annulus, for the hole radius to reinforcing ring thickness ratio, as well as the loading conditions, including loads applied onto the hole boundary and on the plate, far away from the hole. A careful validation of the proposed framework is carried out by comparing the newly developed solution with the results from a number of finite element analyses, documenting a very satisfactory agreement.The solution derived represents a useful tool toward the understanding of the stress fields in polymeric components with reinforced holes and made with fused deposition modelling technologies.

Development of Deep Convolutional Neural Network for Structural Topology Optimization

This research develops a highly effective deep-learning-based surrogate model that can provide the optimum topologies of 2D and 3D structures. In general, structural topology optimization requires plenty of computations because of a large number of finite element analyses to obtain optimal structural layouts by reducing the weight and satisfying the constraints. Therefore, many researchers have developed a deep-learning-based model using the initial static analysis results to predict the optimum designs. However, these studies still considered relatively simple example problems, such as a cantilever plate and MBB beam, even though they required a large number of data to achieve an accurate surrogate model for the simple application. To overcome these limitations, we propose a new framework, which 1) efficiently uses limited data by normalizing it and 2) employs a surrogate model capable of handling more practical cases, such as a 2D panel and 3D stiffened panel subjected to a distributed load, and can be used for local–global structural optimization. In all cases, the developed surrogate models can predict the optimum layouts with structural performance levels equal to those of the structures considered to be ground truths. Also, when the optimal structures were obtained using the proposed method, the total calculation time was reduced by 98% as compared to conventional topology optimization once the convolutional neural network had been trained.

Mapping Methodology for Self and Mutual Inductance Profiles in IPT Systems

Magnetic couplers (MC) are the key element that enable the power transfer over large air gaps in inductive power transfer (IPT) systems. Numerous designs with different coil and core arrangements have been proposed in the literature. However, the MC sizing process still involves several trial and error iterations to meet the desired specifications. This paper presents a profile methodology that uses fitting equations to extrapolate the coupling profiles and minimize the required number of finite element analysis (FEA) simulation results. A non-polarized circular coupler (FLCP) can be characterized as function of the air gap and lateral displacements using only six charging positions, whereas polarized couplers, such as the bipolar (BPP) or double-D pad (DDP), can be characterized using 18 charging positions. The methodology is validated experimentally using the FLCP, and an average error of 3% was found under different charging positions.

Numerical investigation of the effect of slope angle and height on the stability of a slope composed of sandy soil

Slope stability issues are very frequently in civil engineering applications and are commonly encountered in huge and significant projects such as dams, highways and tunnels, etc. This study examines the impact of slope height (H) and slope angle (β) on the stability of loose granular soil slope underlined by dense granular soil layer. For this purpose, a number of finite element analyses were conducted on a full-scale soil slope. The computer program Plaxis 2D code was used which is based on the finite element method (FEM). The granular soils were described by non-linear hardening soil model, which is an advanced elastoplastic stress-strain constitutive soil model. Six different slope angles were investigated and for each angle, six different heights were chosen. In total, twelve series of numerical analyses were executed. In the first six series, it was assumed that there is no surcharge load on the top of the slope. In the second six series, the effect of surcharge load was also investigated. According to numerical analysis results, it was found that the slope height and slope angle have a considerable effect on the safety factor (FS) of the slope. It was also noticed that most of the failure surfaces of the slope were circular and classified as face slope failure. It was observed that by increasing slope height and the slope angle, the FS of the slope decreases and vice versa. In addition, curves and charts have been proposed to easily estimate the FS of loose granular soil slope.

A new simple specimen for mixed-mode (I/II) fracture and fatigue tests: Numerical and experimental studies

In the present investigation, a simple and efficient specimen geometry for conducting mixed mode (I/II) static fracture tests and fatigue crack growth studies has been proposed. No additional complicated fixtures are needed for loading the specimen and it can be used for both metallic and non-metallic materials. Large number of finite element analyses and mixed mode fracture experiments have been conducted. Present results of the experimental studies have been compared with widely used mixed mode (I/II) fracture criteria in terms of fracture toughness. The present experimental results are in very good agreement with the selected mixed mode (I/II) fracture criteria. Results of the present investigation clearly recommend the proposed specimen geometry as a useful mixed mode (I/II) specimen for fracture and fatigue studies.

Multicriteria Optimal Latin Hypercube Design-Based Surrogate-Assisted Design Optimization for a Permanent-Magnet Vernier Machine

This article proposes an efficient surrogate-assisted design optimization method based on a multicriteria optimal Latin hypercube design (LHD) for multi-objective optimization of a surface-mounted permanent-magnet vernier machine (SPMVM). An improved iterated local search (ILS) method is proposed to optimize the spatial distribution uniformity and orthogonality of LHDs so that the data feature over the wide ranges of optimization variables can be captured more efficiently. Using the optimal LHD, a highly generalizable surrogate model can be trained with fewer samples, thus greatly reducing the required number of finite element analysis (FEA) cases and improving the optimization efficiency. A prototype corresponding to the optimal design is built and measured to validate the proposed method.

A computationally efficient surrogate model based robust optimization for permanent magnet synchronous machines

One of the main obstacles to the robust optimization for permanent magnet machines is the high computational burden, which is mainly caused by the robustness evaluation considering the manufacturing uncertainties. In this paper, a sequential sampling Kriging model is adopted to estimate the design robustness, and the problem of high-dimensional variables for the surrogate model because of uncertainties is avoided through adopting the worst-case based approach. To further reduce the number of finite element analyses (FEA) required for constructing a metamodel, a multi-points sequential sampling process with a two-step optimization oriented surrogate model updating algorithm is proposed. Compared with the FEA directly based robust optimization in previous work, similar Pareto Fronts are achieved by adopting the meta-model proposed algorithm but the overall run time reduced by 75%. In the end, an optimization problem for a 1.2 kW motor is considered by applying the proposed algorithm, and two prototypes with deliberately designed tolerances, imitating the worst-case scenarios in the real world, are manufactured. It is found that the worst-case torque ripple is reduced from 7:6% to 4:8% after optimizing when considering the manufacturing uncertainties, and this verifies the accuracy and efficacy of the proposed algorithm.

Research on Bridge Structure Reliability Evaluation due to Vessels Collison Based on a Statistical Moment Method

Damage to bridge structures caused by vessel collision is a risk for bridges crossing water traffic routes. Therefore, safety around vessel collision of existing and planned bridges is one of the key technical problems that must be solved by engineering technicians and bridge managers. In the evaluation of the reliability of the bridge structure, the two aspects of vessel-bridge collision force and structural resistance need to be considered. As there are many influencing parameters, the performance function is difficult to express by explicit function. This paper combines the moment method theory of structural reliability with finite element analysis and proposes a statistical moment method based on finite element analysis for the calculation of vessel-bridge collision reliability, which solves the structural reliability problem with a nonlinear implicit performance function. According to the probability model based on current velocity, vessel velocity, and vessel collision tonnage, the estimate points in the standard normal space are converted into estimate points in the original state space through the Rosenblatt reverse transform. According to the estimate points in the original state space and the simplified dynamic load model of vessel-bridge collision, the sample time-history curve of random vessel-bridge collision force is generated, the dynamic response of the bridge structure and the structural resistance of the bridge are calculated by establishing a finite element model, and the failure probability and reliability index of the bridge structure is calculated according to the fourth-moment method. The statistical moment based on the finite element analysis is based on the finite element analysis and the moment method theory of structural reliability. The statistical moment of the limited performance function is calculated through a quite small amount of confirmatory finite element analysis, and the structural reliability index and failure probability are obtained. The method can be widely used in existing finite element analysis programs, greatly reducing the number of finite element analyses needed and improving the efficiency of structural reliability analysis.

Numerical and Theoretical Modelling of the Web‐Post Buckling of Stainless Steel Cellular Beams

AbstractCellular steel beams are widely used in modern constructions to achieve long spans and to provide passage for service installations such as ducts and cables. The present paper is concerned with the use of stainless steel in cellular beams. In fact, available design methods to calculate the shear strength of web‐post are applicable only to carbon steel that exhibits a linearly‐elastic behaviour with a clear yield point followed by plastic deformation with little amount of strain hardening. Conversely, stainless steel exhibits a non‐linear stress‐strain relationship with high level of strain hardening. Consequently, new design provisions for the web‐post buckling of cellular beams made from stainless steel capable of exploiting the material strain hardening are highly desirable. Since no experimental investigations are available in literature for cellular beams made from stainless steel, finite‐element models have been developed and validated against tests conducted for carbon steel cellular beams. The structural behaviour of stainless steel cellular beams with various geometries and material characteristics is investigated through a large number of finite element analyses and a simple mechanical model for the Web‐Post Buckling (WPB) failure is developed and calibrated against the numerical results to provide the basis of a reliable design method.

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

Topology 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.

An efficient multi-resolution topology optimization scheme for stiffness maximization and stress minimization

This article develops a multi-resolution topology optimization (MTOP) approach based on the solid isotropic material with penalization (SIMP) method, which is effective in obtaining high-resolution designs at low computational cost. The extended finite element method (XFEM) is employed to decouple the analysis mesh, material description and nodal design variables. By the advantage of XFEM at modelling material discontinuity, detailed geometrical features are generated on a coarse analysis mesh. To obtain a clear interface between material grids, a variation of the traditional sensitivity filter is introduced to produce discrete solutions. The low computational costs make the proposed approach appropriate for dealing with problems requiring a high number of finite element analysis (FEA) processes, typically high-resolution/large-scale models, stress minimization, etc. Accurate von Mises stress is calculated on a high number of Gaussian points, making the approach perform better at stress minimization. Then, several 2D and 3D examples optimized by different solvers are illustrated to demonstrate the effectiveness and excellent generality of the proposed approach.

ALGA: Active Learning-Based Genetic Algorithm for Accelerating Structural Optimization

Optimization of complex structures using standard evolutionary algorithms, like genetic algorithm (GA), is known to be computationally expensive, because a very large number of finite element analysis (FEA) must be conducted for each possible structural design during the optimization. In the literature, different pretrained surrogate models have been used to replace the FEA for improving the computational performance of the structural optimization. However, the optimal solution found by the optimizer often depends on the accuracy of the pretrained surrogate model itself. Moreover, large datasets may be needed for getting the required accuracy of the surrogate model. An adaptive machine learning technique called active learning is used in this paper to accelerate the evolutionary optimization of complex structures. An active learner is a machine-learning-based model that can interactively query the outputs of certain data points, whenever the model would be uncertain about those outputs. In the presented approach, the active learner helps the GA by predicting if the possible design is going to be feasible or infeasible, meaning if it satisfies the required constraints or not. If the active learner is uncertain about the output, an actual FEA is conducted, and it improves its own accuracy for future evaluations. The approach does not need a trained surrogate model before the optimization. The active learner adaptively learns about the structure during the optimization to improve the computational performance. The approach is used to optimize the classic 10-bar truss problem, the Hesse function, curvilinearly stiffened panels under buckling and stress constraints, and some benchmark constrained test functions. The results show that the approach has the potential to reduce the total required constraint evaluations by more than 50%.

Reliability-based design optimisation of structural systems using high-order analytical moments

Reliability-based design optimisation paradigm has become increasingly popular to achieve economical yet safer structural designs. However, within the iterative optimisation procedure, it is a challenging problem to simultaneously satisfy both, accuracy and computational efficiency of reliability analysis, particularly for nonlinear or large design problems. Addressing the shortcomings of the mainstream reliability estimation methods, this paper presents a new reliability-based design optimisation method that combines an analytical high-order moment-based uncertainty evaluation with an efficient response surface modelling. The proposed framework allows for the precise calculation of reliability through accurate high-order moments. The fast and accurate reliability estimation in combination with efficient sampling, in turn, reduces the total number of finite element analysis in achieving the final design. The proposed moment-based design optimisation methodology was tested on problems ranging from the design of a simple cantilever to a three-dimensional multistorey steel structure. It outperforms the mainstream methods with higher accuracy and lower computational burden especially when applied to a highly nonlinear numerical problem.

Adaptive continuation solid isotropic material with penalization for volume constrained compliance minimization

In this paper, the traditional decreasing tolerance continuation solid isotropic material with penalization (CSIMP) was extended by providing a way to adapt the penalty step between subproblems, decreasing the number of subproblems solved. Four linearly elastic, volume constrained, compliance minimization problems were used to test the efficacy of the penalty adaptation for different parameter settings. Three of the problems are common 2D test problems and one is 3D. The main factors affecting the efficacy of the penalty adaptation were identified. Experimental results confirmed that the penalty adaptation successfully reduces the number of finite element analysis (FEA) simulations needed to converge to the optimal solution when using the decreasing tolerance CSIMP (Dec-Tol CSIMP), with exponentially decaying tolerance. In particular, the number of FEA simulations required by Dec-Tol CSIMP was cut down by an average of 28.8% with no more than 4.1% increase in the objective value in the worst case. Finally, a mathematical and experimental treatment of the effect of xmin on the convergence of the SIMP algorithm was given, with recommendations for choosing a suitable value for xmin.

Numerical and analytical analyses of high-strength steel cellular beams: A discerning approach

The behaviour of cellular beams made from normal and high strength steel with various geometries is investigated through a large number of finite element analyses and a simple mechanical model for the Web-Post Buckling (WPB) failure is developed and analysed in order to highlight the factors which influence its occurrence and development for both normal and High-Strength (HS) steels. The performed FE analyses and the proposed modelling, once calibrated, allow to shed some light on the characteristics of the phenomenon and to provide the basis of a reliable design method to predict shear buckling of web-post of cellular beams made both of mild and HS steel.