Elastic Finite Element Method Research Articles

A discontinuous Galerkin Finite Element Method for linear elasticity using a mixed integration scheme to circumvent shear‐locking

AbstractShear‐locking is a significant problem when using the Finite Element Method (FEM) with standard lower order Langrangian shape functions. To avoid this effect we introduce the discontinuous Galerkin Finite Element Method (dG‐FEM) for linear elasticity. In addition to a standard integration scheme for the dG‐FEM we develop a mixed integration scheme and compare both with established finite elements using a bending dominated benchmark. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DEM/FEM Simulations of Dynamic Response of Projectile Penetrating into Granular Medium

Dynamic elastic Finite Element Method (FEM) and Discrete element method (DEM) simulations are carried out to investigate dynamic penetration of a projectile into a target of granular medium. It was found that the highly densified region of granular medium was generated just ahead of the projectile and began to propagate spherically with much higher velocity than that of projectile which leaves relatively rarefied medium region. This propagation phenomenon was probably the result of a collision and momentum transfer between particles in target granular medium. The propagation velocity of the densified region decreased during penetration as depending not only on the packing ratio of target medium but also on the projectile velocity. The resistance force of projectile was also investigated in the case of penetration of projectiles with various body lengths. The resistance force increased rapidly and reached to the peak. The peak value was expressed in terms of momentum change of target particles. The resistance force decreased periodically after the peak value. The period clearly depended on the length of projectile. It is obvious that this was caused by the stress wave reverberations in the projectiles with various body lengths.

An Adaptive Hybrid Stress Transition Quadrilateral Finite Element Method for Linear Elasticity

In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid stress quadrilateral elements with 5 to 7 nodes. In particular, we derive a priori error estimation for the 5node transition hybrid stress element to show that it is free from Poisson-locking, in the

Beam Buckling Analysis by Nonlocal Integral Elasticity Finite Element Method

In this study, a finite element method (FEM) based on the size dependent nonlocal integral elasticity theory is implemented for buckling analysis of nanoscaled beams with various boundary conditions. The method is based on the principle of total potential energy. The variations of buckling load with respect to the scaling effect parameter and to the length-to-thickness ratio are investigated. Furthermore, the effect of attenuation function type on the buckling load is examined. The results are compared with the corresponding solutions of governing stability equations which are derived in the context of nonlocal differential elasticity theory. It is found that the small scale coefficient has a noticeable effect on the buckling load of nanobeams.

Estimating inherent deformation in thin-plate Al-alloy joint by means of inverse analysis with the help of cutting technique

The elastic finite element method based on inherent strain theory has been recognized as an effective tool to estimate the total welding deformation for large and complex welded structures. When this computational approach is employed to predict welding deformation in a weldment, one prerequisite is that the inherent deformations of each welded joint included in the welded structure should be known beforehand. The inverse analysis method based on the combination of measuring technology and finite element method can be used to obtain the inherent deformations for various welded joints. However, if buckling distortion occurs in a welded joint, it will be difficult for this method to accurately obtain the inherent deformations especially in thin-plate joints. To overcome this difficulty, an improved inverse analysis method with the help of cutting technique was developed in the current study. The effectiveness of the proposed method was demonstrated through obtaining the inherent deformations in an Al-alloy thin-plate joint with buckling distortion.

Analysis of Fatigue Crack Growth in Ship Structural Details

Abstract Fatigue failure avoidance is a goal that can be achieved only if the fatigue design is an integral part of the original design program. The purpose of fatigue design is to ensure that the structure has adequate fatigue life. Calculated fatigue life can form the basis for meaningful and efficient inspection programs during fabrication and throughout the life of the ship. The main objective of this paper is to develop an add-on program for the analysis of fatigue crack growth in ship structural details. The developed program will be an add-on script in a pre-existing package. A crack propagation in a tanker side connection is analyzed by using the developed program based on linear elastic fracture mechanics (LEFM) and finite element method (FEM). The basic idea of the developed application is that a finite element model of this side connection will be first analyzed by using ABAQUS and from the results of this analysis the location of the highest stresses will be revealed. At this location, an initial crack will be introduced to the finite element model and from the results of the new crack model the direction of the crack propagation and the values of the stress intensity factors, will be known. By using the calculated direction of propagation a new segment will be added to the crack and then the model is analyzed again. The last step will be repeated until the calculated stress intensity factors reach the critical value.

A Robust Weak Galerkin Finite Element Method for Linear Elasticity with Strong Symmetric Stresses

Abstract This paper proposes and analyzes a weak Galerkin (WG) finite element method with strong symmetric stresses for two- and three-dimensional linear elasticity problems on conforming or nonconforming polygon/polyhedral meshes. The WG method uses piecewise-polynomial approximations of degrees k ( ≥ 1 ${\geq 1}$ ) for the stress, k + 1 ${k+1}$ for the displacement, and k for the displacement trace on the inter-element boundaries. It is shown to be equivalent to a hybridizable discontinuous Galerkin (HDG) finite element scheme. We show that the WG methods are robust in the sense that the derived a priori error estimates are optimal and uniform with respect to the Lamé constant λ. Numerical experiments confirm the theoretical results.

Low-Order Discontinuous Petrov--Galerkin Finite Element Methods for Linear Elasticity

This paper analyzes lowest-order discontinuous Petrov--Galerkin (dPG) finite element methods (FEM) for the Navier--Lame equations with different norms and side restrictions. The focus is on the direct proof of a discrete inf-sup condition for a low-order test-search space. The low-order finite element spaces in the ultraweak formulation involve the piecewise constant and affine ansatz functions and discontinuous piecewise affine test functions in two and three space dimensions with Neumann boundary conditions or the pure Dirichlet problem. Those lowest-order discretizations for linear elasticity allow for a direct proof of the discrete inf-sup condition and a complete a priori and a posteriori error analysis which is robust in the incompressible limit as $\lambda \rightarrow \infty$. Numerical experiments with uniform and adaptive mesh-refinements investigate $\lambda$-robustness and confirm that one scheme is locking-free.

Study on elastic-wall fluid cavity resonant frequency of Helmholtz underwater acoustic transducer

Helmholtz resonators are commonly used as underwater acoustic transducers to transmit low-frequency, great power acoustic waves at fluid cavity resonant frequency. Therefore, it is an important problem in the study of how to calculate accurately the fluid cavity resonant frequency of Helmholtz resonator, especially when the Helmholtz resonator is used in underwater acoustic environment where Helmholtz transducers cannot be designed using the classical air acoustic Helmholtz resonator theory. The elasticity of the cavity wall has to be considered because it has a strong influence on the fluid cavity resonant frequency at low frequency band. In this paper, the method of calculating accurately fluid cavity resonant frequency is researched for low-frequency Helmholtz underwater transducers. A Helmholtz resonator is a slender cylindrical shell, the boundary condition of its two ends is free: one side is a radiating port, and the other side is considered as a rigid baffle. Firstly, the fluid cavity resonant frequency of the rigid wall Helmholtz resonator is given, then the radial mechanical impedance of the slender cylindrical shell is derived based on the wave equations. Elasticity of the cavity wall is introduced into the acoustic impedance of fluid cavity in the form of additional impedance. Based on the low-frequency lumped parameter model of the slender cylindrical shell, additional acoustic impedance expression of elastic cavity wall is derived, complete equivalent circuit diagram of elastic Helmholtz underwater transducers is developed, taking into account the elasticity of the cavity wall. Based on the equivalent circuit, the accurate fluid cavity resonant frequency formula has been derived; the formula shows that both the structure size and material characteristics of the cavity wall have influence on the fluid cavity resonant frequency. The thinner the cavity wall, the lower the fluild cavity resonant frequency; and the smaller the Young's modulus of the material, the lower the fluild cavity resonant frequency. To verify the accuracy of the present theory, several slender cylindrical shell models with different wall thickness, materials, and wall length are investigated by both elastic theory method and finite element method (using ANSYS software). These results reveal that the elastic theory results are in excellent agreement with the finite element simulation results. That means, compared to traditional rigid wall theory results, the results from elastic theory in this paper is much closer to the real situation. This conclusion can provide a theoretical support for the accurate design of low-frequency elastic Helmholtz underwater acoustic transducers.

Perbandingan Analisis Lendutan Pelat dengan Menggunakan Metode Beam on Elastic Foundation (BoEF) dan Finite Element Method (FEM)

The aim of this study was to compare deflection plates are supported by soil by using the method of Beam on Elastic Foundation (BoEF) and Finite Element Method (FEM). To validated the methods, used data from laboratory testing of the loading plate models. For the calculation of deflection plates on elastic (soil) foundation, the accuracy of determining the modulus of subgrade reaction will greatly affect the calculation of deflection plate. Deflection calculation used Finite Element Method and BoEF method gave deflections, where close enough to those of experimental result. Both methods can be used to estimate the plate deflection.

Multi-step forming simulation and experiment of swing arms for torsion beam

Numerical simulations of bending, performing, and hydroforming processes of automotive swing arms for torsion beam were conducted using finite element analysis. The process parameters such as bending radius, mandrels, loading paths, and calibration pressure were optimized in the simulation. In addition, closing force was predicted by die stress–strain analysis using the elastic finite element method. Subsequently, the bending, performing, and hydroforming experiments were performed based on the simulation results. The experimental results indicated that swing arms could be fabricated when the bending radius, calibration pressure, and closing force would be of 120 mm, 150 MPa, and 15,000 kN, respectively. Finally, swing arms with high thickness uniformity were obtained and the thickness distribution between numerical and experimental results was well consistent.

Structural Dynamics and Attitude Control of a Solar Sail Using Tip Vanes

This paper delves into the structural and attitude dynamics of a cord-mat square solar sail being controlled by two-degree-of-freedom tip-vane actuation. The paper’s main goal is to simulate and analyze the behavior of a solar sail under a tip-vane attitude control scheme using a geometrically nonlinear elastic finite element method model of the sail. The controller/structural interaction is of particular interest, as the control solution of the two-degree-of-freedom tip-vane actuation is based on a flat, inflexible sail. The sail structure is further augmented by a wrinkling model for handling the membranes under negative strain. The model is further augmented by the disturbance forces produced by the reflective sail membrane itself. A combined, dynamic simulation of all of the aforementioned are performed to analyze the performance of the control system as a whole.

Coupled DDD–FEM modeling on the mechanical behavior of microlayered metallic multilayer film at elevated temperature

To investigate the mechanical behavior of the microlayered metallic thin films (MMMFs) at elevated temperature, an enhanced discrete-continuous model (DCM), which couples rather than superposes the two-dimensional climb/glide-enabled discrete dislocation dynamics (2D-DDD) with the linearly elastic finite element method (FEM), is developed in this study. In the present coupling scheme, two especial treatments are made. One is to solve how the plastic strain captured by the DDD module is transferred properly to the FEM module as an eigen-strain; the other is to answer how the stress field computationally obtained by the FEM module is transferred accurately to the DDD module to drive those discrete dislocations moving correctly. With these two especial treatments, the interactions between adjacent dislocations and between dislocation pile-ups and inter-phase boundaries (IBs), which are crucial to the strengthening effect in MMMFs, are carefully taken into account. After verified by comparing the computationally predicted results with the theoretical solutions for a dislocation residing in a homogeneous material and nearby a bi-material interface, this 2D-DDD/FEM coupling scheme is used to model the tensile mechanical behaviors of MMMFs at elevated temperature. The strengthening mechanism of MMMFs and the layer thickness effect are studied in detail, with special attentions to the influence of dislocation climb on them.

Mechanics of fatigue crack initiation in submicron-thick freestanding copper films

The mechanics of fatigue crack initiation in roughly 500-nm-thick freestanding copper (Cu) films were investigated by using single-side-edge-notched specimens and elastic finite element method (FEM) analyses. By applying cyclic loading at a stress ratio R=0, an intrusion/extrusion was formed near a notch root, and a fatigue crack then initiated at the intrusion/extrusion, which penetrated the film in the thickness direction on a slip plane parallel to a Σ3 twin boundary. Local stress distributions were evaluated by three-dimensional FEM analyses, taking account of the individual grain shape and crystal orientation around the fatigue crack initiation sites. The results revealed that a fatigue crack was initiated on slip systems where (i) the slip deformation penetrated the film in the thickness direction without being blocked by grain boundaries or twin boundaries, and (ii) a high resolved shear stress occurred under the conditions in (i). The number of cycles to fatigue crack initiation increased as the intensity of the resolved shear stress field at the fatigue crack initiation site decreased. The resolved shear stress required for fatigue crack initiation in the Cu films is roughly one order of magnitude higher than that in a bicrystal or single-crystal bulk Cu of 30–35MPa.

Experimental Measurement of Residual Stress on Thermal Spray Coatings with Moire Interferometry and Hole-Drilling Method

Residual stress is one of the important factors in thermally sprayed deposits which affects both processing and performances. In the present study, the hole-drilling method and moire interferometry were used to determine the residual stress of thermally sprayed coatings to overcome certain limitations of the strain rosette version of hole drilling. The methodology was established based on the elastic theory and finite element method. The residual displacement was measured by moire interferometry and the residual stress of the thermally sprayed coating was calculated. The results have demonstrated that moire interferometry for surface displacement caused by hole-drilling is high sensitive, reliable and stable.

Bridge stress calculation based on the dynamic response of coupled train–bridge system

Stress responses under vehicle loads are of great significance during the life-cycle of a bridge. The accurate identification of these responses is necessary for the bridge design, construction, assessment, maintenance, and rehabilitation. This paper presents a numerical approach for the stress analysis of railway bridges based on train–bridge coupled dynamics. A coupled train-bridge system model composed of a 3D vehicle model, a 3D bridge model established with the direct stiffness method, and an assumed wheel–rail contact relationship considering random excitations due to track irregularities, is developed. Based on the results of the train–bridge coupled analysis, bridge dynamic stress responses are then computed by elastic finite element method. The field measurement data of a 32m simply-supported concrete bridge on a heavy haul railway is analyzed to validate the accuracy of the proposed approach. Additionally, the effect of two key parameters (i.e., the train speed and track irregularity) of the train–bridge coupled vibration analysis is discussed. The approach is illustrated on an existing railway steel bridge with low lateral stiffness. The stress time histories of bridge members are computed and compared to those obtained by using the moving concentrated load model, with an emphasis on the stress responses induced by lateral vibrations.

钢筋混凝土桥墩的二阶效应影响研究

本文扼要介绍了钢筋混凝土桥墩二阶效应计算方法的发展及应用。相对于仅适用于简单结构的偏心距增大系数法，基于构件折减刚度的弹性有限元法，采用折减系数考虑非线性的影响，具有更广泛的适用性。针对该弹性有限元法，本文进一步对比了中美混凝土设计规范中折减系数的不同取值。在数值算例中，用三种不同方法分别计算了二阶效应对单墩墩底弯矩的影响，计算结果表明偏心距增大系数法的计算结果偏于保守。 The development and application of reinforced concrete pier second-order effect calculation method have been introduced in this paper. Compared with the law of the change of moment merely implied on simple structures, the elastic finite element method, based on reduced rigidity and using reduction factor to consider the no-linear effect, has an extensive applicability. As for the elastic finite element method, this paper compared the different values of reduction factors in the concrete design code of China and the United States. In numerical examples, three methods are applied to calculate the influence of second-order effect on the moment at the bottom of single pier. The results show that the law of the change of moment is conservative.

OS0506-141 三次元接合角部のスカラーパラメーター解析手法の精度改善

The asymptotic solution of the singular stress around a three dimensional corner between dissimilar materials was analyzed using the H-integral method. However, we could not obtain the accurate scalar parameters of asymptotic solution for some problems. In this study, we investigated what reduced the accuracy of the solution and how to improve the accuracy. The eigen values and eigen vectors of the asymptotic solution was analyzed by the eigenvalue decomposition of the finite element model of a corner. After that we analyzed a target problem using the elastic finite element method, and performed the H-integral to obtain the scalar parameters. We found out that the some integral equations related with the H-integral, which should be zero, were not zero when we obtained inaccurate scalar parameters. The integral values decrease with refining the finite element meshes for the eigenvalue decomposition, and the obtained scalar parameters approached constant values. The eigenvalue decomposition demanded very fine finite element meshes to obtain the accurate values for some problems.

Simulation of dynamic response of projectile and granular target

In the present study, the three-dimensional elastic discrete element method (DEM) and the elastic finite element method (FEM) analysis were, respectively, applied to the randomly distributed identical spheres as a granular target and to the cylindrical projectiles in order to clarify dynamic response during penetration. In the target, it was found that highly densified region was formed just ahead of the projectile and began to propagate spherically at much higher velocity than that of projectile leaving relatively rarefied region. It was also found that the peak resistance during penetration was closely related to the initial formation of densified region and was expressed in terms of momentum change of target particles accelerated by the projectile. Stress wave propagation in the projectiles with various body lengths was investigated during penetration and was discussed in connection with dynamic response of target particles ahead of the projectile. Effect of mechanical properties of projectile on the peak resistance was also investigated and was understood in connection with dynamic behavior of target particles.

A Staggered Cell-Centered Finite Element Method for Compressible and Nearly-Incompressible Linear Elasticity on General Meshes

We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its triangular submesh, the scheme can be constructed from a general mesh in which the displacement is approximated by piecewise linear (P1) functions on the dual submesh and, in the case of nearly incompressible problems, the pressure is approximated by piecewise constant (P0) functions on the dual mesh. The scheme is cell centered in the sense that the solution can be computed by cell unknowns of the primal mesh (for the displacement) and of the dual mesh (for the pressure). The method is presented within a rigorous theoretical framework to show stability and convergence. In particular, for the nearly incompressible case, stability is proved by using the macroelement technique. Numerical results show that the method, compared with other methods, is effective in terms of accuracy and computational cost.