Comparative assessments of strain measures for nonlinear analysis of truss structures at large deformations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Marcelo Greco ◽  
Daniel Henrique Nunes Peixoto
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sine Function ◽  
Strain Measure ◽  
Content Type ◽  
Hyperbolic Sine ◽  
Structural Applications ◽  
Strain Measures ◽  
Hyperbolic Sine Function ◽  
Element Method

PurposeIn this paper the use of classical strain measures in analysis of trusses at finite deformations will be discussed. The results will be compared to the ones acquired using a novel strain measure based on the Hyperbolic Sine function. Through the evaluation of results, algebraic development and graph analysis, the properties of the Hyperbolic Sine strain measure will be examined.Design/methodology/approachThrough graph plotting, comparisons between the novel strain measure and the classic ones will be made. The formulae for the implementation of the Hyperbolic Sine strain measure into a positional finite element method are developed. Four engineering applications are presented and comparisons between results obtained using all strain measures studied are made.FindingsThe proposed strain measure, Hyperbolic Sine, has objectivity and symmetry. The linear constitutive model formed by the Hyperbolic Sine strain and its conjugated stress presents an increasing stiffness, both in compression and tension, a behavior that can be useful in the modeling of several materials.Research limitations/implicationsThe structural analysis performed on the four examples of trusses in this article did not consider the variation of the cross-sectional area of the elements or the buckling phenomenon, moreover, only elastic behavior is considered.Originality/valueThe present article proposes the use of a novel strain measure family, based on the Hyperbolic Sine function and suitable for structural applications. Mathematical expressions for the use of the Hyperbolic Sine strain measure are established following the energetic concepts of the positional formulation of the finite element method.

Parallel finite-element method using domain decomposition and Parareal for transient motor starting analysis

2019 ◽  
Vol 38 (5) ◽  
pp. 1507-1520 ◽  
Author(s):  
Yasuhito Takahashi ◽  
Koji Fujiwara ◽  
Takeshi Iwashita ◽  
Hiroshi Nakashima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parallel Computing ◽  
Domain Decomposition ◽  
Parallel Computation ◽  
Domain Decomposition Method ◽  
Space Time ◽  
Content Type ◽  
Parallel Performance ◽  
Element Method

Purpose This paper aims to propose a parallel-in-space-time finite-element method (FEM) for transient motor starting analyses. Although the domain decomposition method (DDM) is suitable for solving large-scale problems and the parallel-in-time (PinT) integration method such as Parareal and time domain parallel FEM (TDPFEM) is effective for problems with a large number of time steps, their parallel performances get saturated as the number of processes increases. To overcome the difficulty, the hybrid approach in which both the DDM and PinT integration methods are used is investigated in a highly parallel computing environment. Design/methodology/approach First, the parallel performances of the DDM, Parareal and TDPFEM were compared because the scalability of these methods in highly parallel computation has not been deeply discussed. Then, the combination of the DDM and Parareal was investigated as a parallel-in-space-time FEM. The effectiveness of the developed method was demonstrated in transient starting analyses of induction motors. Findings The combination of Parareal with the DDM can improve the parallel performance in the case where the parallel performance of the DDM, TDPFEM or Parareal is saturated in highly parallel computation. In the case where the number of unknowns is large and the number of available processes is limited, the use of DDM is the most effective from the standpoint of computational cost. Originality/value This paper newly develops the parallel-in-space-time FEM and demonstrates its effectiveness in nonlinear magnetoquasistatic field analyses of electric machines. This finding is significantly important because a new direction of parallel computing techniques and great potential for its further development are clarified.

Semi-analytical finite element method for simulating chemical dissolution-front instability problems in fluid-saturated porous media

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chongbin Zhao ◽  
B.E. Hobbs ◽  
Alison Ord
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Chemical Dissolution ◽  
Saturated Porous Media ◽  
Content Type ◽  
Front Instability ◽  
Fluid Saturated Porous Media ◽  
Dissolution Front ◽  
Element Method

PurposeThe objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.Design/methodology/approachThe porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.FindingsThe direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.Originality/valueAnalytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

Stress, strain and displacement analysis of geodetic and conventional fuselage structure for future passenger aircraft

2019 ◽  
Vol 91 (6) ◽  
pp. 814-819
Author(s):  
Zdobyslaw Jan Goraj ◽  
Mariusz Kowalski ◽  
Bartlomiej Goliszek
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weight Reduction ◽  
Composite Structures ◽  
Lattice Structure ◽  
Small Displacement ◽  
Structure Stability ◽  
Outer Diameter ◽  
Content Type ◽  
Element Method

Purpose This paper aims to present the results of calculations that checked how the longerons and frames arrangement affects the stiffness of a conventional structure. The paper focuses only on first stage of research – analysis of small displacement. Main goal was to compare different structures under static loads. These results are also compared with the results obtained for a geodetic structure fuselage model of the same dimensions subjected to the same internal and external loads. Design/methodology/approach The finite element method analysis was carried out for a section of the fuselage with a diameter of 6.3 m and a length equal to 10 m. A conventional and lattice structure – known as geodetic – was used. Findings Finite element analyses of the fuselage model with conventional and geodetic structures showed that with comparable stiffness, the weight of the geodetic fuselage is almost 20 per cent lower than that of the conventional one. Research limitations/implications This analysis is limited to small displacements, as the linear version of finite element method was used. Research and articles planned for the future will focus on nonlinear finite element method (FEM) analysis such as buckling, structure stability and limit cycles. Practical implications The increasing maturity of composite structures manufacturing technology offers great opportunities for aircraft designers. The use of carbon fibers with advanced resin systems and application of the geodetic fuselage concept gives the opportunity to obtain advanced structures with excellent mechanical properties and low weight. Originality/value This paper presents very efficient method of assessing and comparison of the stiffness and weight of geodetic and conventional fuselage structure. Geodetic fuselage design in combination with advanced composite materials yields an additional fuselage weight reduction of approximately 10 per cent. The additional weight reduction is achieved by reducing the number of rivets needed for joining the elements. A fuselage with a geodetic structure compared to the classic fuselage with the same outer diameter has a larger inner diameter, which gives a larger usable space in the cabin. The approach applied in this paper consisting in analyzing of main parameters of geodetic structure (hoop ribs, helical ribs and angle between the helical ribs) on fuselage stiffness and weight is original.

A MSFEM to simulate the eddy current problem in laminated iron cores in 3D

2019 ◽  
Vol 38 (5) ◽  
pp. 1667-1682 ◽  
Author(s):  
Karl Hollaus
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eddy Current ◽  
Eddy Currents ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Three Dimensions ◽  
Magnetic Vector Potential ◽  
Content Type ◽  
Element Method

Purpose The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by finite elements leads to extremely large nonlinear systems of equations impossible to solve with present computer resources reasonably. The purpose of this study is to show that the multiscale finite element method (MSFEM) overcomes this difficulty. Design/methodology/approach A new MSFEM approach for eddy currents of laminated nonlinear iron cores in three dimensions based on the magnetic vector potential is presented. How to construct the MSFEM approach in principal is shown. The MSFEM with the Biot–Savart field in the frequency domain, a higher-order approach, the time stepping method and with the harmonic balance method are introduced and studied. Findings Various simulations demonstrate the feasibility, efficiency and versatility of the new MSFEM. Originality/value The novel MSFEM solves true three-dimensional eddy current problems in laminated iron cores taking into account of the edge effect.

Dynamic tensile process of blended fabric using finite element method

2020 ◽  
Vol 32 (5) ◽  
pp. 707-724
Author(s):  
Xuzhong Su ◽  
Xinjin Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Experimental Testing ◽  
Woven Fabrics ◽  
Weft Yarn ◽  
Tensile Fracture ◽  
Content Type ◽  
Tensile Process ◽  
Simulation Results ◽  
Element Method

PurposeTensile property is one basic mechanics performance of the fabric. In general, not only the tensile values of the fabric are needed, but also the dynamic changing process under the tension is also needed. However, the dynamic tensile process cannot be included in the common testing methods by using the instruments after fabric weaving.Design/methodology/approachBy choosing the weft yarn and warp yarn in the fabric as the minimum modeling unit, 1:1 finite element model of the whole woven fabrics was built by using AutoCAD software according to the measured geometric parameters of the fabrics and mechanical parameters of yarns. Then, the fabric dynamic tensile process was simulated by using the ANSYS software. The stress–strain curve along the warp direction and shrinkage rate curve along the weft direction of the fabrics were simulated. Meanwhile, simulation results were verified by comparing to the testing results.FindingsIt is shown that there are four stages during the fabric tensile fracture process along the warp direction under the tension. The first stage is fabric elastic deformation. The second stage is fabric yield deformation, and the change rate of stress begins to slow down. The third stage is fiber breaking, and the change of stress fluctuates since the breaking time of the fibers is different. The fourth stage is fabric breaking.Originality/valueIn this paper, the dynamic tensile process of blended woven fabrics was studied by using finite element method. Although there are differences between the simulation results and experimental testing results, the overall tendency of simulation results is the same as the experimental testing results.

Variational multi-scale finite element method for the two-phase flow of polymer melt filling process

2019 ◽  
Vol 30 (3) ◽  
pp. 1407-1426 ◽  
Author(s):  
Xuejuan Li ◽  
Ji-Huan He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Method ◽  
Two Phase Flow ◽  
Polymer Melt ◽  
Phase Flow ◽  
Filling Process ◽  
Two Phase ◽  
Content Type ◽  
Element Method

Purpose The purpose of this paper is to develop an effective numerical algorithm for a gas-melt two-phase flow and use it to simulate a polymer melt filling process. Moreover, the suggested algorithm can deal with the moving interface and discontinuities of unknowns across the interface. Design/methodology/approach The algebraic sub-grid scales-variational multi-scale (ASGS-VMS) finite element method is used to solve the polymer melt filling process. Meanwhile, the time is discretized using the Crank–Nicolson-based split fractional step algorithm to reduce the computational time. The improved level set method is used to capture the melt front interface, and the related equations are discretized by the second-order Taylor–Galerkin scheme in space and the third-order total variation diminishing Runge–Kutta scheme in time. Findings The numerical method is validated by the benchmark problem. Moreover, the viscoelastic polymer melt filling process is investigated in a rectangular cavity. The front interface, pressure field and flow-induced stresses of polymer melt during the filling process are predicted. Overall, this paper presents a VMS method for polymer injection molding. The present numerical method is extremely suitable for two free surface problems. Originality/value For the first time ever, the ASGS-VMS finite element method is performed for the two-phase flow of polymer melt filling process, and an effective numerical method is designed to catch the moving surface.

An enriched formulation of isogeometric analysis applied to the dynamical response of bars and trusses

2020 ◽  
Vol 37 (7) ◽  
pp. 2439-2466
Author(s):  
Mateus Rauen ◽  
Roberto Dalledone Machado ◽  
Marcos Arndt
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Isogeometric Analysis ◽  
Computer Aided Design ◽  
Numerical Solutions ◽  
Dynamical Response ◽  
Generalized Finite Element Method ◽  
Content Type ◽  
High Convergence Rate ◽  
Element Method

Purpose This study aims to present a new hybrid formulation based on non-uniform rational b-splines functions and enrichment strategies applied to free and forced vibration of straight bars and trusses. Design/methodology/approach Based on the idea of enrichment from generalized finite element method (GFEM)/extended finite element method (XFEM), an extended isogeometric formulation (partition of unity isogeometric analysis [PUIGA]) is conceived. By numerical examples the methods are tested and compared with isogeometric analysis, finite element method and GFEM in terms of convergence, error spectrum, conditioning and adaptivity capacity. Findings The results show a high convergence rate and accuracy for PUIGA and the advantage of input enrichment functions and material parameters on parametric space. Originality/value The enrichment strategies demonstrated considerable improvements in numerical solutions. The applications of computer-aided design mapped enrichments applied to structural dynamics are not known in the literature.

On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bruna Caroline Campos ◽  
Felício Bruzzi Barros ◽  
Samuel Silva Penna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Numerical Integration ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Content Type ◽  
Integration Techniques ◽  
Integration Strategies ◽  
Element Method

Purpose The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered. Design/methodology/approach Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results. Findings Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities. Originality/value This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

The modified characteristics finite element method for time-dependent Darcy-Brinkman problem

2018 ◽  
Vol 36 (1) ◽  
pp. 356-376 ◽  
Author(s):  
Cheng Liao ◽  
Pengzhan Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Double Diffusion ◽  
Diffusion Problem ◽  
Content Type ◽  
Characteristics Method ◽  
Complicated Model ◽  
Velocity Pressure ◽  
First Time ◽  
Element Method

Purpose This study aims to capture the effective behavior of double-diffusion problem, which arises from the combined heat and mass transfer in porous medium and develop the modified characteristics finite element method. Design/methodology/approach The proposed finite element method deals with the nonlinear term temporal term by modified characteristics method. Then, the authors compute the velocity, pressure, temperature and concentration using the decoupled technique. Finally, to show the efficiency of the method, the authors give some numerical examples. Findings From the numerical results, one can see that the method has a good accuracy, which shows that the method can simulate this Darcy–Brinkman problem well. Originality/value The originality lies in the fact that the proposed scheme is the first time for solving the Darcy–Brinkman problem, which is a more complicated model, and includes the velocity, pressure, temperature and concentration.

Determination of the auxiliary anode position via finite element method in impressed current cathodic protection

2019 ◽  
Vol 66 (4) ◽  
pp. 432-438
Author(s):  
Yingwei Liu ◽  
Zhongwu Zhang ◽  
Yang Zhang ◽  
Jianneng Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cathodic Protection ◽  
Measurement Errors ◽  
Optimization Method ◽  
Content Type ◽  
Protection Method ◽  
Impressed Current ◽  
Impressed Current Cathodic Protection ◽  
Element Method

Purpose It is a challenge in the design to determine the feasible anode position and the supply current when the hull is protected by the impressed current cathodic protection method. It is difficult to obtain these parameters through traditional experimental methods due to the huge hull surface area and geometric complexity. This study aims to solve the problem by finite element method. Design/methodology/approach First, a great number of experiments need to be conducted; second, experiments are empirical; finally, there exist measurement errors, etc. All these factors make the experimental results less reliable. The application of the finite element method, combined with other technologies, is expected to overcome these deficiencies. In this paper, the combined Matlab and Comsol method was used to calculate various anode positions and corresponding protection areas with a series of input current conditions. The calculation is implemented via the script in Matlab. Findings As a result, the best design can be obtained. The results show that the method provided in this paper can replace the experiment to a certain extent, save human and material resources and reduce the design time. The method also can be applied to other similar fields, having a good universality. Originality/value This optimization method can be extended to other areas of relevant production and research, having a good universality.

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