Displacement-based Finite Element Analysis Research Articles

New displacement-based finite element analysis method for predicting the surface residual stress generated by ultrasonic nanocrystal surface modification

Peening techniques can be applied to relieve high tensile residual stress, which is one of the main causes of primary water stress corrosion cracking (PWSCC). Ultrasonic nanocrystal surface modification (UNSM) is a peening technique that generates a high compressive residual stress on the surface of a structure. Finite element (FE) analysis can be utilized for quantitative surface stress prediction according to the UNSM in various materials and loading conditions. In this paper, a new method to predict the surface residual stress generated by UNSM process through FE analysis is proposed. In order to accurately simulate the UNSM process through FE analysis, it is necessary to define an equivalent displacement calculation method that can replace the complex load states of UNSM. For this, we proposed the new equivalent displacement calculation method based on the contact mechanics theory and the energy conservation law. The new equivalent displacement calculation method was validated by comparing the indentation depth obtained by single-path UNSM FE analyses and experiments under various loading conditions. The actual UNSM process is carried out in multiple paths over a large area of the structure. By applying the new equivalent displacement calculation method, the compressive residual stresses were calculated through multi-path UNSM FE analyses and compared with the results obtained from the multi-path UNSM experiments. The surface residual stress results of the experiments and analyses showed good agreement, and it was confirmed that the UNSM process can be simulated well if the new equivalent displacement calculation method is used for the FE analysis.

Normally loaded inclined strip anchors in cohesionless soil

Plate anchors are among the most effective anchorage systems that are widely used to resist horizontal and inclined uplift loads in many offshore and onshore applications. Previous research on plate anchors has largely focused on the horizontal or vertical breakout problems, with limited attention directed towards obtaining a full characterization of the effects of anchor orientation angle. The present study utilizes displacement-based finite element analyses to investigate the stability and performance of strip anchor embedded in cohesionless soil for plate inclination angles ranging from 0° to 90° from horizontal, where the applied load is normal to and acts at the center of the plate. This study investigates the effects of scale and roughness, along with the geometry of the failure mechanism for various plate orientations and embedment depths. The analyses, presented in terms of a non-dimensional breakout factor Nq, show that the breakout factor increases significantly with an increase in the inclination, especially for angles greater than 45° in loose sand and greater than 60° in dense sand. The analyses also show that scale effects (anchor width) can affect capacity. Finite element analyses have been used to introduce simple design charts relating the breakout factor to the embedment depth and relative density. Comparisons to experimental and numerical studies showed good agreement.

Finite element analyses of slope stability problems using non-associated plasticity

In recent years, finite element analyses have increasingly been utilized for slope stability problems. In comparison to limit equilibrium methods, numerical analyses do not require any definition of the failure mechanism a priori and enable the determination of the safety level more accurately. The paper compares the performances of strength reduction finite element analysis (SRFEA) with finite element limit analysis (FELA), whereby the focus is related to non-associated plasticity. Displacement-based finite element analyses using a strength reduction technique suffer from numerical instabilities when using non-associated plasticity, especially when dealing with high friction angles but moderate dilatancy angles. The FELA on the other hand provides rigorous upper and lower bounds of the factor of safety (FoS) but is restricted to associated flow rules. Suggestions to overcome this problem, proposed by Davis (1968), lead to conservative FoSs; therefore, an enhanced procedure has been investigated. When using the modified approach, both the SRFEA and the FELA provide very similar results. Further studies highlight the advantages of using an adaptive mesh refinement to determine FoSs. Additionally, it is shown that the initial stress field does not affect the FoS when using a Mohr-Coulomb failure criterion.

Multiphysics computational analysis of white-etch cracking failure mode in wind turbine gearbox bearings

Wind energy is currently one of the most promising and the fastest-growing installed alternative-energy production technologies. It is anticipated that by 2030, at least 20% of the US energy needs will be provided by this form of energy. The economics of wind energy require that wind turbines (convertors of wind energy into electrical energy) be able to operate for at least 20 years, with only regular maintenance. Unfortunately, many wind turbines require major repairs after only 3–5 years in service, mainly due to the failure of their gear boxes. It is this lack of gear box reliability which is currently compromising wind energy economics. In the present work, a multiphysics computational methodology has been developed and used to analyze the problem of white-etch cracking, one of the key processes responsible for the premature failure of gearbox roller bearings. The multiphysics methodology includes: (a) quantum-mechanical calculations of the hydrogen dissolution and the accompanying grain boundary embrittlement phenomena; (b) atomistic-level kinetic Monte Carlo analysis of hydrogen diffusion from the crack wake into the adjacent unfractured material; (c) cohesive zone type modeling of the intergranular fracture processes; and (d) a conventional displacement-based finite element analysis of the kinematic and structural response of the bearing under service loading conditions. The results obtained clearly revealed the operation of the white-etch cracking phenomena and their possible interaction with the conventional rolling-contact fatigue damage processes.

Treatment of locking behaviour for displacement-based finite element analysis of composite beams

In the displacement based finite element analysis of composite beams that consist of two Euler-Bernoulli beams juxtaposed with a deformable shear connection, the coupling of the displacement fields may cause oscillations in the interlayer slip field and reduction in optimal convergence rate, known as slip-locking. In this study, the B-bar procedure is proposed to alleviate the locking effects. It is also shown that by changing the primary dependent variables in the mathematical model, to be able to interpolate the interlayer slip field directly, oscillations in the slip field can be completely eliminated. Examples are presented to illustrate the performance and the numerical characteristics of the proposed methods.

Alleviation of parasitic slip in finite element analysis of composite beams

In the conventional displacement-based finite element analysis of composite beams that consist of two Euler–Bernoulli beams juxtaposed with a deformable shear connection, the coupling of the transverse and longitudinal displacement fields may cause oscillations in interlayer slip field and reduction in optimal convergence rate, known as slip locking. This locking phenomenon is typical of multi-field problems of this type, and is known to produce erroneous results for the displacement based finite element analysis of composite beams based on cubic transverse and linear longitudinal interpolation fields. In this study, a very simple and novel procedure is introduced to eliminate the parasitic slip in the finite element analysis of composite beams. A systematic solution of the differential equations of equilibrium is also provided, and an exact element is developed in the paper. Numerical results presented illustrate the accuracy gained based on the proposed modification to the basic finite element formulation. Solutions based on the exact element provide benchmark results for the performance of the proposed formulation.

Modeling of nonlinear viscoelastic–viscoplastic frictional contact problems

This paper presents a nonlinear time-dependent computational model for analyzing the quasistatic response of viscoelastic–viscoplastic frictional contact problems. Both material and geometrical nonlinearities are considered in the framework of the Lagrangian description. The material nonlinearity is due to the time–stress-dependency of the constitutive equation, while the geometrical nonlinearity is due to large displacements and rotations, but small strains. The model is derived based on an implicit time-integration method within a general displacement-based finite element analysis. The nonlinear Schapery’s single integral model is used to model the viscoelastic part, while the Perzyna model is adopted model the viscoplastic part. The exponential form of the Prony series is used to represent the transient component of the viscoelastic creep compliance, since it permits hereditary effects to be computed recursively. In addition, an incremental form of the viscoplastic strain component is derived in the framework of associative viscoplasticity based on implicit integration scheme. Throughout the contact interface, friction is simulated using a local-nonlinear friction law, while the Lagrange multiplier method is adopted to model the inequality contact constraints. In a presented case study, the complete contact configuration and internal stresses are analyzed. Results show the significant effects of material nonlinearity, viscoplastic flow, and friction on the response of contact problems.

Optimization of Cut-Out Shape on Composite Plate Under In-Plane Shear Loading

The wing in flight condition is subjected to heavy aerodynamic loads that in turn lead to a shear flow over the wing ribs that support it. Cut-outs change the mechanical behavior of plates, as they redistribute the stresses and are influenced by the shape of the cut-out. A three-dimensional displacement-based finite element analysis is performed to study the symmetric, laminated composite plate of 20 layers. The analysis is performed to obtain the in-plane and out of plane performances of the laminate. Five basic cut-out geometries, viz., circle, square, diamond, ellipse with major axis along the y-axis, and another ellipse with major axis along the x axis were used for the numerical analysis. A cut-out geometry is generated based on the results of analyses performed on five basic geometries to optimize the performance. The optimized cut-out is associated with the least Tsai-Hill and Hashin failure index as compared with the five basic geometries.

Displacement-based finite element formulations for material-nonlinear analysis of composite beams and treatment of locking behaviour

In this paper a numerical procedure is developed for the material-nonlinear analysis of composite beams composed of two Euler–Bernoulli beams juxtaposed with a deformable shear connection. In the displacement-based finite element analysis of composite beams, however, the coupling of the transverse and longitudinal displacement fields may cause oscillations in the interlayer slip field and reduction in optimal convergence rate, known as slip-locking. A very simple and novel procedure is introduced to develop an assumed strain formulation, which alleviates slip-locking in the numerical analysis of composite beams and provides superconvergent points for slip values. It is also shown that by changing the primary variable fields of Newmark's mathematical model, to interpolate the slip field directly, slip-locking can be completely eliminated. Numerical examples are presented to illustrate the performances and the numerical characteristics of the proposed methods.

Locking-free finite element formulation for steel-concrete composite members

In the conventional displacement-based finite element analysis of composite beam-columns that consist of two Euler-Bernoulli beams juxtaposed with a deformable shear connection, the coupling of the transverse and longitudinal displacement fields may cause oscillations in interlayer slip field and reduction in optimal convergence rate, known as slip-locking. This locking phenomenon is typical of multi-field problems of this type, and is known to produce erroneous results for the displacement based finite element analysis of composite beam-columns based on cubic transverse and linear longitudinal interpolation fields. In this paper it will be shown that by simple change of the pair of dependent variables in the formulation the locking behaviour can be alleviated. An example is presented to illustrate the effects of connection stiffness on the behaviour of composite beams and the results show that the proposed approach is efficient in alleviating the locking behaviour.

Curvature‐ and displacement‐based finite element analyses of flexible slider crank mechanisms

AbstractThe paper presents the applications of the curvature‐ and displacement‐based finite element methods to flexible slider crank mechanisms. The displacement‐based method usually needs more elements or high‐degree polynomials to obtain highly accurate solutions. The curvature‐based method assumes a polynomial to approximate a curvature distribution, and the expressions are investigated to obtain the displacement and rotation distributions. During the process, the boundary conditions associated with displacement, rotation, and curvature are imposed, which leads the great reduction of the number of degrees of freedom that are required. The numerical results demonstrate that the errors obtained by applying the curvature‐based method are much smaller than those by applying the displacement‐based method, based on the comparison of the same number of degrees of freedom. Copyright © 2008 John Wiley & Sons, Ltd.

A piecewise linear Galerkin approach to stress analysis of nearly incompressible materials

The displacement-based finite element analysis of nearly incompressible materials is susceptible to the volumetric locking and pressure instability. As an effective remedy for these problems, a Galerkin formulation of the stress governing equations based on separate weak statements for displacement and pressure, has been derived. Apart from the various existing techniques, like the non-conforming, high order, or mixed methods, the proposed Galerkin approach is inherently free from the constraints imposed on the selection of discrete approximation spaces and permits a robust and stable implementation of piecewise linear trial and test functions. The accuracy and stability of the method are tested on a model problem with the available closed-form solution. Copyright © 2000 John Wiley & Sons, Ltd.

Effective stress-based finite element error estimation for composite bodies

This paper presents a discretization error estimator for displacement-based finite element analysis applicable to multi-material bodies such as composites. The proposed method applies a specific stress continuity requirement across the intermaterial boundary consistent with physical principles. This approach estimates the discretization error by comparing the discontinuous finite element effective stress function with a smoothed ( C 0 continuous) effective stress function for non-intermaterial boundary elements with a smoothed pseudo-effective stress function for elements which lie on the intermaterial boundary. Examples are presented which illustrate the effectiveness of the multi-material error estimator. The pointwise pseudo-effective stress and the L 2 norm of the estimated stress error are seen to converge with mesh refinement, while Zienkiewicz and Zhu's error estimator failed to converge for elements on the intermaterial boundary due to the physically admissible stress discontinuities that exist on the intermaterial boundary.

Effective stress-based finite element error estimation for composite bodies

This paper presents a discretization error estimator for displacement-based finite element analysis applicable to multi-material bodies such as composites. The proposed method applies specific stress continuity requirement across the intermaterial boundary consistent with physical principles. This approach estimates the discretization error by comparing the discontinuous finite element effective stress function with a smoothed ( C 0 continuous) effective stress function for non-intermaterial boundary elements and with a smoothed pseudo effective stress function for elements which lie on the intermaterial boundary. Examples are presented which illustrate the effectiveness of the multi-material error estimator. The pointwise pseudo effective stress and the L 2 norm of the estimated stress error are seen to converge with mesh refinement, while the Zienkiewicz and Zhu's error estimator failed to converge for elements on the intermaterial boundary due to the physically admissible stress discontinuities that exist on the intermaterial boundary.

Stress analysis of a thick fibre-reinforced plastic laminated square plate containing two elliptical holes under transverse uniform loading

A displacement-based finite element analysis applicable for thick laminated composite plate is described. An isoparametric quadratic quadrilateral element with eleven degrees of freedom per node is used in this analysis. The finite element formulation is then used for the analysis of stresses of a simply supported finite laminated square plate containing two elliptical holes under transverse uniform loading. The results are compared with the exact elasticity solutions, which demonstrate the validity of the method. The variation of the stress concentration factor due to the change of the distance between the holes, the hole size and the plate thickness is presented in graphical form and discussed.

Forthcoming papers

This paper presents a nonlinear time-dependent computational model for analyzing the quasistatic response of viscoelastic–viscoplastic frictional contact problems. Both material and geometrical nonlinearities are considered in the framework of the Lagrangian description. The material nonlinearity is due to the time–stress-dependency of the constitutive equation, while the geometrical nonlinearity is due to large displacements and rotations, but small strains. The model is derived based on an implicit time-integration method within a general displacement-based finite element analysis. The nonlinear Schapery’s single integral model is used to model the viscoelastic part, while the Perzyna model is adopted model the viscoplastic part. The exponential form of the Prony series is used to represent the transient component of the viscoelastic creep compliance, since it permits hereditary effects to be computed recursively. In addition, an incremental form of the viscoplastic strain component is derived in the framework of associative viscoplasticity based on implicit integration scheme. Throughout the contact interface, friction is simulated using a local-nonlinear friction law, while the Lagrange multiplier method is adopted to model the inequality contact constraints. In a presented case study, the complete contact configuration and internal stresses are analyzed. Results show the significant effects of material nonlinearity, viscoplastic flow, and friction on the response of contact problems.