Traditional Finite Element Analysis Research Articles

English

Textile composites consist of interlaced tows, which are impregnated with a matrix material and then cured. The interlacing of the tows offers the potential for increased through-thickness strength compared to conventional laminated composites. However, one disadvantage of textile composites is the difficulty in predicting their per formance due to the complex geometry of their internal architectures. Finite element analysis (FEA) has become an effective means to predict the response of complex textile composite structures. When an attempt is made to perform a conventional FEA, one of the tough issues faced is how to deal with the topologically complex internal geometries. To overcome this difficult issue, a domain superposition technique (DST) has been proposed to implement free vibration analysis of woven composite structures. The significant advantage of the DST over traditional FEA is that it does not need to directly deal with the likely degenerated resin-rich region, thus the DST model is much easier to establish. Numerical results show that DST predictions correlate excellently with traditional FEAs.

Finite Element Analysis and Experiment Study on the Lorry Crane Telescopic Arm

Traditional mechanics calculation and finite element analysis are performed to estimate the stress and distribution for each section of the telescopic arm in the operation of lorry crane. Through theoretical analysis, the working strength of the lorry crane telescopic arm can be obtained. Meanwhile experiment study is performed to verify the rationality of the finite analysis results, The results show that the telescopic boom has higher security, thus to provide theoretical support for design of the lorry crane telescopic arm.

Discontinuous Galerkin Methods for Isogeometric Analysis for Elliptic Equations on Surfaces

We propose a method that combines isogeometric analysis (IGA) with the discontinuous Galerkin (DG) method for solving elliptic equations on 3-dimensional (3D) surfaces consisting of multiple patches. DG ideology is adopted across the patch interfaces to glue the multiple patches, while the traditional IGA, which is very suitable for solving partial differential equations (PDEs) on (3D) surfaces, is employed within each patch. Our method takes advantage of both IGA and the DG method. Firstly, the time-consuming steps in mesh generation process in traditional finite element analysis (FEA) are no longer necessary and refinements, including $$h$$ -refinement and $$p$$ -refinement which both maintain the original geometry, can be easily performed by knot insertion and order-elevation (Farin, in Curves and surfaces for CAGD, 2002). Secondly, our method can easily handle the cases with non-conforming patches and different degrees across the patches. Moreover, due to the geometric flexibility of IGA basis functions, especially the use of multiple patches, we can get more accurate modeling of more complex surfaces. Thus, the geometrical error is significantly reduced and it is, in particular, eliminated for all conic sections. Finally, this method can be easily formulated and implemented. We generally describe the problem and then present our primal formulation. A new ideology, which directly makes use of the approximation property of the NURBS basis functions on the parametric domain rather than that of the IGA functions on the physical domain (the former is easier to get), is adopted when we perform the theoretical analysis including the boundedness and stability of the primal form, and the error analysis under both the DG norm and the $${\mathcal {L}}^{2}$$ norm. The result of the error analysis shows that our scheme achieves the optimal convergence rate with respect to both the DG norm and the $${\mathcal {L}}^{2}$$ norm. Numerical examples are presented to verify the theoretical result and gauge the good performance of our method.

Utilizing a Simple Numerical Model in Discrete Element Analysis to Simulate Flow Time and Number Tests of Asphalt Mixes

During the past decades, many numerical models have been used to predict responses of asphalt mixes under different types of loading. Some of these models were simple due to practicality but overestimated the response of asphalt mixes. On the other hand, sophisticated but effective numerical models have been developed to address the shortcomings of the simpler models, and were used mostly in finite element analysis (FEA). However, these models were complicated and not user friendly. Recently, the approach of the discrete element method (DEM) was adopted. Unlike traditional FEA, DEM can simulate crack propagation by allowing the separation of elements in the simulated models. Understanding these challenges, this study was initiated to investigate the utilization of a simple visco-elasto-plastic model that had been used successfully in predicting deformation in asphalt mixes using the DEM embedded in Particle Flow Code in Two Dimensions (PFC2D) software simulations. Simulation results, when compared to flow time (FT) and number (FN) test results, showed that this model could simulate actual tests, thus predicting deformation of asphalt mixes using the DEM on a larger scale.

Dedicated algorithm and software for the integrated analysis of AC and DC electrical outputs of piezoelectric vibration energy harvesters

DC electrical outputs of a piezoelectric vibration energy harvester by nonlinear rectifying circuitry can hardly be obtained either by any mathematical models developed so far or by finite element analysis. To address the issue, this work used an equivalent electrical circuit model and newly developed an algorithm to efficiently identify relevant circuit parameters of arbitrarily-shaped cantilevered piezoelectric energy harvesters. The developed algorithm was then realized as a dedicated software module by adopting ANSYS finite element analysis software for the parameters identification and the Tcl/Tk programming language for a graphical user interface and linkage with ANSYS. For verifications, various AC electrical outputs by the developed software were compared with those by traditional finite element analysis. DC electrical outputs through rectifying circuitry were also examined for varying values of the smoothing capacitance and load resistance.

Meshfree modeling of dynamic response of mechanical structures

Transient nature of the loading conditions applied to the structural components makes dynamic analysis one of the important components in the design-analysis cycle. Time-varying forces and accelerations can substantially change stress distributions and cause a premature failure of the mechanical structures. In addition, it is also important to determine dynamic response of the structural elements to the frequency of the applied loads. In this paper we describe the first application of the meshfree Solution Structure Method (SSM) to the structural dynamics problems. SSM is a meshfree method which enables construction of the solutions to the engineering problems that satisfy exactly all prescribed boundary conditions. This method is capable of using spatial meshes that do not conform to the shape of a geometric model. Instead of using the grid nodes to enforce boundary conditions, it employs distance fields to the geometric boundaries and combines them with the basis functions and prescribed boundary conditions at run time. This defines unprecedented geometric flexibility of the SSM as well as the complete automation of the solution procedure. In the proposed approach we will use SSM to enforce initial and boundary conditions, while transient behavior is enforced by time marching schemes used to solve systems of ordinary differential equations. In the paper we will explain the key points of the SSM as well as investigate the accuracy and convergence of the proposed approach by comparing our results with the ones obtained using traditional finite element analysis. Despite in this paper we are dealing with 2D in-plane vibrations, the proposed approach has a straightforward application to model vibrations of 3D structures.

An Integrated Simulation System for Building Structures

In this paper, an integrated simulation system for building structures is presented to satisfy the engineering requirements for high performance simulation. It is a coalition of the traditional design softwares and general finite element analysis (FEA) softwares. This system is developed in the platform of Intel Fortran, using the programming language of Fortran2003/2008. For simplicity, it would be introduced and discussed briefly in the following article. And combining with YJK and ABAQUS, this system is implemented to perform dynamic analysis for a high-rise building. Its capacity and validity would be demonstrated by the numerical results.

Mass scaling and stable time step estimates for isogeometric analysis

SummaryMetal stamping is one of the most cost effective manufacturing methods for producing precision parts. The precision of the parts is a function of the uniformity of the material used for the blank and the design of the dies. During the metal stamping process, the blank undergoes large, inelastic deformations, and once it is removed from the dies, springs back to a shape different from the die. This spring back must be accounted for in the design of the die, and its prediction is a major challenge in computational mechanics. Isogeometric analysis, which uses the same basis functions as the computer‐aided design programs used to design the shape of the part, is an attractive alternative to traditional finite element analysis for metal stamping. Mass scaling, and the underlying stable time step estimates, that are commonly used in metal stamping simulations are presented for isogeometric analysis. Example calculations are presented to demonstrate the effectiveness of isogeometric analysis in metal stamping. Copyright © 2014 John Wiley & Sons, Ltd.

Critical-Buckling-Load Assessment of Drillstrings in Different Wellbores by Use of the Explicit Finite-Element Method

Summary Previous theoretical formulations for sinusoidal and helical buckling of drillstrings vary significantly and are mostly proposed for frictionless pipes without tool joints. Finite-element-analysis (FEA) methods have the ability to consider geometric details and nonlinearities. However, traditional FEA methods use shell or solid elements for this problem and are computationally expensive. In this paper, an explicit FEA that is based on beam and connector elements implemented in the Abaqus software (2012) is used to study the problem in different wellbores. The wellbore geometry, formation stiffness, friction load, and friction-induced torque are modeled with connector elements. A typical drillstring in vertical, inclined, horizontal, and curved wellbores is simulated, and the explicit FEA results for sinusoidal- and helical-buckling loads are compared with different theoretical formulations and experimental results in the literature. The effects of length, inclination angle, and string effective weight caused by buoyancy as well as the effect of tool joints in straight and curved wellbores are also studied and compared with present formulations and published experimental results. A full-scale well-buckling test has also been simulated, and load-transfer data are compared with the real-world results. Overall, it is demonstrated that the use of explicit FEA can efficiently study drillstring buckling behavior in straight- and curved-wellbore conditions.

Superconvergence Analysis of Finite Element Method for Onlinear Klein-Gordon Equation

The standard finite elements of degree p over the rectangular meshes are applied to a non-linear Klein-Gordon equation. By utilizing the properties of interpolation on the element, high accuracy analysis and derivative delivery techniques with respect to time t instead of the traditional Ritz projection operator, which is an indispensable tool in the traditional finite element analysis, the supercloseproperty with order is obtained. Furthermore, the superconvergence result is derived through the postprocessing approach.

Two-Dimensional Structural Topology Optimization Based on Isogeometric Analysis

In this paper, the isogeometric analysis is applied to two-dimensional structural topology optimization instead of traditional finite element analysis. By treating the corresponding element density of knot spans as design variables, the topology optimization model is formulated based on SIMP method. Then the optimization problem is solved using the method of moving asymptotes. As demonstrated by examples, the proposed method can be used for two-dimensional topology optimization. And the results show that checkerboard patterns can be controlled.

Multi-objective optimization of sheet metal forming die using FEA coupled with RSM

Present study describes the approach of applying response surface methodology (RSM) with a Pareto-based multi-objective genetic algorithm to assist engineers in optimization of sheet metal forming. In many studies, finite element analysis and optimization technique have been integrated to solve the optimal process parameters of sheet metal forming by transforming multi objective problem into a single-objective problem. This paper aims to minimize objective functions of fracture and wrinkle simultaneously. Design variables are blank-holding force and draw-bead geometry (length and diameter). Response surface model has been used for design of experiment and finding relationship between variables and objective functions. Forming limit diagram (FLD) has been used to define objective functions. Finite element analysis applied for simulating the process. Proposed approach has been investigated on a cross-shaped cup drawing case and it has been observed that it is more effective and accurate than traditional finite element analysis method and the ‘trial and error’ procedure.

Multi-objective Optimization of Sheet Metal Forming Die Using Genetic Algorithm Coupled with RSM and FEA

Present study describes the approach of applying response surface methodology (RSM) with a Pareto-based multi-objective genetic algorithm to assist engineers in optimization of sheet metal forming. In many studies, finite element analysis and optimization technique have been integrated to solve the optimal process parameters of sheet metal forming by transforming multi-objective problem into a single-objective problem. This paper aims to minimize objective functions of fracture and wrinkle simultaneously. Design variables are blank-holding force and draw-bead geometrical parameters (length and diameter). RSM has been used for design of experiment and finding relationship between variables and objective functions. Forming limit diagram has been used to define objective functions. Finite element analysis applied for simulating the process. Proposed approach has been investigated on a fuel tank drawing part and it has been observed that it is more effective and accurate than traditional finite element analysis method and the “trial and error” procedure.

Meshfree natural vibration analysis of 2D structures

Determination of resonance frequencies and vibration modes of mechanical structures is one of the most important tasks in the product design procedure. The main goal of this paper is to describe a pioneering application of the solution structure method (SSM) to 2D structural natural vibration analysis problems and investigate the numerical properties of the method. SSM is a meshfree method which enables construction of the solutions to the engineering problems that satisfy exactly all prescribed boundary conditions. This method is capable of using spatial meshes that do not conform to the shape of a geometric model. Instead of using the grid nodes to enforce boundary conditions, it employs distance fields to the geometric boundaries and combines them with the basis functions and prescribed boundary conditions at run time. This defines unprecedented geometric flexibility of the SSM as well as the complete automation of the solution procedure. In the paper we will explain the key points of the SSM as well as investigate the accuracy and convergence of the proposed approach by comparing our results with the ones obtained using analytical methods or traditional finite element analysis. Despite in this paper we are dealing with 2D in-plane vibrations, the proposed approach has a straightforward generalization to model vibrations of 3D structures.

High accuracy analysis of the characteristic‐nonconforming FEM for a convection‐dominated transport problem

A low order characteristic‐nonconforming finite element method is proposed for solving a two‐dimensional convection‐dominated transport problem. On the basis of the distinguish property of element, that is, the consistency error can be estimated as order O(h2), one order higher than that of its interpolation error, the superclose result in broken energy norm is derived for the fully discrete scheme. In the process, we use the interpolation operator instead of the so‐called elliptic projection, which is an indispensable tool in the traditional finite element analysis. Furthermore, the global superconvergence is obtained by using the interpolated postprocessing technique. Lastly, some numerical experiments are provided to verify our theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd.

Application of neural networks for the prediction of cartilage stress in a musculoskeletal system

Traditional finite element (FE) analysis is computationally demanding. The computational time becomes prohibitively long when multiple loading and boundary conditions need to be considered such as in musculoskeletal movement simulations involving multiple joints and muscles. Presented in this study is an innovative approach that takes advantage of the computational efficiency of both the dynamic multibody (MB) method and neural network (NN) analysis. A NN model that captures the behavior of musculoskeletal tissue subjected to known loading situations is built, trained, and validated based on both MB and FE simulation data. It is found that nonlinear, dynamic NNs yield better predictions over their linear, static counterparts. The developed NN model is then capable of predicting stress values at regions of interest within the musculoskeletal system in only a fraction of the time required by FE simulation.

외팔보 압전 진동 에너지 수확 장치의 직류 전기 출력 해석을 위한 전용 알고리즘 개발

For most applications of the vibration energy harvesting technology as in wireless sensor networks for smart buildings and plants, the evaluation of DC output performance of vibration energy harvesters is typically required. However, there is no dedicated algorithm for the evaluation. The lack of a dedicated algorithm results from difficulties in the direct incorporation of nonlinear rectifying and regulating circuitry into finite element models of piezoelectric vibration energy harvesters. In this study, we develop a dedicated algorithm and present software based on it for the evaluation of not only AC but also DC electrical quantities. Here, an equivalent electrical circuit model is employed. The COMSOL multiphysics simulation tool is adopted for extracting equivalent electrical circuit parameters of a piezoelectric vibration energy harvester and MATLAB is used to make a graphical user interface. The AC voltage and power outputs calculated by the proposed algorithm under various conditions are compared with those by a traditional finite element analysis. The DC output voltage and power through a rectifier are obtained for varying values of smoothing capacitance and external resistance.

KNEE JOINT CONTACT MECHANICS IN A MALALIGNED LIMB: AN INTEGRATED FINITE ELEMENT AND IN VITRO STUDY

Traditional finite element (FE) analysis is computationally demanding. The computational time becomes prohibitively long when multiple loading and boundary conditions need to be considered such as in musculoskeletal movement simulations involving multiple joints and muscles. Presented in this study is an innovative approach that takes advantage of the computational efficiency of both the dynamic multibody (MB) method and neural network (NN) analysis. A NN model that captures the behavior of musculoskeletal tissue subjected to known loading situations is built, trained, and validated based on both MB and FE simulation data. It is found that nonlinear, dynamic NNs yield better predictions over their linear, static counterparts. The developed NN model is then capable of predicting stress values at regions of interest within the musculoskeletal system in only a fraction of the time required by FE simulation.

A partition of unity FEM for time‐dependent diffusion problems using multiple enrichment functions

SUMMARYAn enriched partition of unity FEM is developed to solve time‐dependent diffusion problems. In the present formulation, multiple exponential functions describing the spatial and temporal diffusion decay are embedded in the finite element approximation space. The resulting enrichment is in the form of a local asymptotic expansion. Unlike previous works in this area where the enrichment must be updated at each time step, here, the temporal decay in the solution is embedded in the asymptotic expansion. Thus, the system matrix that is evaluated at the first time step may be decomposed and retained for every next time step by just updating the right‐hand side of the linear system of equations. The advantage is a significant saving in the computational effort where, previously, the linear system must be reevaluated and resolved at every time step. In comparison with the traditional finite element analysis with p‐version refinements, the present approach is much simpler, more efficient, and yields more accurate solutions for a prescribed number of DoFs. Numerical results are presented for a transient diffusion equation with known analytical solution. The performance of the method is analyzed on two applications: the transient heat equation with a single source and the transient heat equation with multiple sources. The aim of such a method compared with the classical FEM is to solve time‐dependent diffusion applications efficiently and with an appropriate level of accuracy. Copyright © 2012 John Wiley & Sons, Ltd.

Fuzzy Multi-Objective Optimization for Die Structures Design in Sheet Metal Forming

Abstract: Finite element analysis and fuzzy multi-objective optimization technique have been integrated to solve the die structure design of sheet metal forming by transforming fuzzy multi-objective problem into a normal optimization problem. A mathematical model of fuzzy optimization for bending die was established. A fuzzy goal set was constructed. The fuzziness of multi-objective functions and constraints were defined. The optimal solution and optimal constraint value of individual objective function in the feasible field were found using the genetic algorithms. An electronic part bending case shows that this approach is more effective and accurate than traditional finite element analysis method and the ‘trial and error’ procedure.