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Journal articles on the topic 'Membrane and shear locking'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Tang, Yi Qun, Zhi Hua Zhou, and Siu Lai Chan. "Nonlinear Beam-Column Element Under Consistent Deformation." International Journal of Structural Stability and Dynamics 15, no. 05 (May 27, 2015): 1450068. http://dx.doi.org/10.1142/s0219455414500680.

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A new nonlinear beam-column element capable of considering the shear deformation is proposed under the concept of consistent deformation. For the traditional displacement interpolation function, the beam-column element produces membrane locking under large deformation and shear locking when the element becomes slender. To eliminate the membrane and shear locking, force equilibrium equations are employed to derive the displacement function. Numerical examples herein show that membrane locking in the traditional nonlinear beam-column element could cause a considerable error. Comparison of the present improved formulae based on the Timoshenko beam theory with that based on the Euler–Bernoulli beam theory indicates that the present approach requires several additional parameters to consider shear deformation and it is suitable for computer analysis readily for incorporation into the frames analysis software using the co-rotational approach for large translations and rotations. The examples confirm that the proposed element has higher accuracy and numerical efficiency.

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2

Swamy Naidu, N. V., and B. Sateesh. "Improved Bilinear Degenerated Shell Element." International Journal of Computational Methods 12, no. 02 (March 2015): 1550004. http://dx.doi.org/10.1142/s0219876215500048.

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The development of a new four node 24 degree of freedom bilinear degenerated shell element is presented for the analysis of shell structures. The present finite element formulation considers the assumed covariant transverse shear strains to avoid the shear locking problem and the assumed covariant membrane strains, which are separated from covariant in-plane strains, to overcome the membrane locking problem. The formulation also includes the deviation of the normal torsional rotation of the mid surface in the governing equation. This element is free from serious shear and membrane locking problems and undesirable spurious kinematic deformation modes. The element is tested for rigid body modes and distorted edges to meet the patch test requirements. The versatility and accuracy of this new degenerated shell element is demonstrated by solving several numerical examples for thick and thin plates.

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3

Yunhua, Luo. "Explanation and elimination of shear locking and membrane locking with field consistence approach." Computer Methods in Applied Mechanics and Engineering 162, no. 1-4 (August 1998): 249–69. http://dx.doi.org/10.1016/s0045-7825(97)00346-0.

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4

Bucalem, Miguel Luiz, and Klaus-Ju¨rgen Bathe. "Locking Behavior of Isoparametric Curved Beam Finite Elements." Applied Mechanics Reviews 48, no. 11S (November 1, 1995): S25—S29. http://dx.doi.org/10.1115/1.3005077.

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We present a study of the membrane and shear locking behavior in an isoparametric curved beam element. The objective is to gain insight into the locking phenomenon, specially membrane locking, of continuum based degenerated shell elements. This is possible since the isobeam element is the one-dimensional analogue of the continuum based shell element. In this context, reduced integration and mixed interpolation schemes are briefly examined. Such a study can be a valuable aid when developing new shell elements.

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5

Tessler, Alexander, and Luciano Spiridigliozzi. "Resolving membrane and shear locking phenomena in curved shear-deformable axisymmetric shell elements." International Journal for Numerical Methods in Engineering 26, no. 5 (May 1988): 1071–86. http://dx.doi.org/10.1002/nme.1620260506.

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6

Polat, Cengiz. "A Parametric Study for Four Node Bilinear EAS Shell Elements." Journal of Mechanics 26, no. 4 (December 2010): 431–38. http://dx.doi.org/10.1017/s1727719100004639.

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ABSTRACTA locking free formulation of 4-node bilinear shell element and its application to shell structures is demonstrated. The Enhanced Assumed Strain (EAS) method based on three-field variational principle of Hu-Washizu is used in the formulation. Transverse shear locking and membrane locking are circumvented by means of enhancing the displacement-dependent strain field with extra assumed strain field. Several benchmark shell problems are analyzed.

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7

Miazio, Łukasz, and Grzegorz Zboiński. "A Posteriori Detection of Numerical Locking in hpq-Adaptive Finite Element Analysis." Applied Sciences 10, no. 22 (November 20, 2020): 8247. http://dx.doi.org/10.3390/app10228247.

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The proposed detection algorithms are assigned for the hpq-adaptive finite element analysis of the solid mechanics problems affected by the locking phenomena. The algorithms are combined with the M- and hpq-adaptive finite element method, where M is the element model, h denotes the element size parameter, and p and q stand for the longitudinal and transverse approximation orders within an element. The applied adaptive scheme is extended with the additional step where the locking phenomena are a posteriori detected, assessed and resolved. The detection can be applied to shear, membrane, or shear–membrane locking phenomena. The removal of the undesired influence of the numerical locking on the problem solution is based on p-enrichment of the mesh. The detection algorithm is also enriched with the locking assessment algorithm which is capable of determination of the optimized value of p which is sufficient for the phenomena removal. The detection and assessment algorithms are based on a simple sensitivity analysis performed locally for the finite elements of the thin-walled domain. The sensitivity analysis lies in comparison of the element solutions corresponding to two values of the order p, namely current and potentially eliminating the locking. The local solutions are obtained from the element residual method. The elaborated algorithms are original, relatively simple, extremely reliable, and highly effective.

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8

Belytschko, Ted, Henryk Stolarski, Wing Kam Liu, Nicholas Carpenter, and Jame S. J. Ong. "Stress projection for membrane and shear locking in shell finite elements." Computer Methods in Applied Mechanics and Engineering 51, no. 1-3 (September 1985): 221–58. http://dx.doi.org/10.1016/0045-7825(85)90035-0.

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9

Jung, Woo-Young, and Sung-Cheon Han. "An 8-Node Shell Element for Nonlinear Analysis of Shells Using the Refined Combination of Membrane and Shear Interpolation Functions." Mathematical Problems in Engineering 2013 (2013): 1–16. http://dx.doi.org/10.1155/2013/276304.

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An improved 8-node shell finite element applicable for the geometrically linear and nonlinear analyses of plates and shells is presented. Based on previous first-order shear deformation theory, the finite element model is further improved by the combined use of assumed natural strains and different sets of collocation points for the interpolation of the different strain components. The influence of the shell element with various conditions such as locations, number of enhanced membranes, and shear interpolation is also identified. By using assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, to characterize the efficiency of these modifications of the 8-node shell finite elements, numerical studies are carried out for the geometrically linear and non-linear analysis of plates and shells. In comparison to some other shell elements, numerical examples for the methodology indicate that the modified element described locking-free behavior and better performance. More specifically, the numerical examples of annular plate presented herein show good validity, efficiency, and accuracy to the developed nonlinear shell element.

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10

Kwon, Y. D., N. S. Goo, and B. S. Lim. "Resolution of Defects in Degenerated Shell Elements Through Modification of Gauss Integration." International Journal of Modern Physics B 17, no. 08n09 (April 10, 2003): 1877–83. http://dx.doi.org/10.1142/s0217979203019812.

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In this paper, the modified Gauss integration method is developed to eliminate the shear and membrane locking phenomena of the degenerated shell element. The behavior of the element based on the Mindlin/Reissner theory in plates and shells sometimes causes a problem. In displacement-based shell elements, the full integration of stiffness matrices leads to a 'locking' or over-stiff behavior. The selective or reduced integration procedures may often overcome these difficulties, while overstiff solutions may still occur in the analysis with a highly constrained boundary. Except for the six zero-energy modes associated with shell rigid body movements, during the reduced integration of the stiffness matrices, many extra zero spurious energy modes are introduced due to reduced integration. This is a serious defect of degenerated shell element. In previous studies, several methods such as the addition of nonconforming displacement modes, an assumed strain method, and hybrid and mixed elements have been introduced in an attempt to overcome these difficulties. In this study a newly modified Gauss integration method combining both a selective and a weight-modified integration is suggested. Numerical experiments show that the new selective integration and weight-modified integration rule is very effective in eliminating the shear and membrane locking in static and modal analyses, and removes spurious zero-energy modes as well. Also, the effectiveness of proposed shell element is tested by applying it to some example problems. We solved post-buckling problem by the Riks arc-length method and dynamic problem by the Newmark's time integration method, as well as static problems.

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11

Kim, Nam-Il. "Shear and Membrane Locking-Free Thin-Walled Curved Beam Element Based on Assumed Strain Fields#." Mechanics Based Design of Structures and Machines 38, no. 3 (July 30, 2010): 273–99. http://dx.doi.org/10.1080/15397731003670576.

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12

Park, K. C., and G. M. Stanley. "A Curved C0 Shell Element Based on Assumed Natural-Coordinate Strains." Journal of Applied Mechanics 53, no. 2 (June 1, 1986): 278–90. http://dx.doi.org/10.1115/1.3171752.

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A curved C0 shell element is presented, which corrects several deficiencies in existing quadratic shell elements. The improvements realized in the present element include rank sufficiency without transverse shear locking, consistent membrane strain interpolation that admits inextensional bending without reduced integration, and adequate representation of curvature effects to capture the important membrane-bending coupling. The element can be constructed either by a nine-point integration rule or by a four-point integration rule with the proper rank compensating terms. Numerical experiments with the present element on several benchmark problems indicate that the element yields accurate and reliable solutions without any ostensible deficiency. The element is recommended for production analysis of shell structures.

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13

Saffari, H., and R. Tabatabaei. "A Finite Circular Arch Element Based on Trigonometric Shape Functions." Mathematical Problems in Engineering 2007 (2007): 1–19. http://dx.doi.org/10.1155/2007/78507.

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The curved-beam finite element formulation by trigonometric function for curvature is presented. Instead of displacement function, trigonometric function is introduced for curvature to avoid the shear and membrane locking phenomena. Element formulation is carried out in polar coordinates. The element with three nodal parameters is chosen on curvature. Then, curvature field in the element is interpolated as the conventional trigonometric functions. Shape functions are obtained as usual by matrix operations. To consider the boundary conditions, a transformation matrix between nodal curvature and nodal displacement vectors is introduced. The equilibrium equation is written by minimizing the total potential energy in terms of the displacement components. In such equilibrium equation, the locking phenomenon is eliminated. The interesting point in this method is that for most problems, it is sufficient to use only one element to obtain the solution. Four examples are presented in order to verify the element formulation and to show the accuracy and efficiency of the method. The results are compared with those of other concepts.

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14

Saffari, H., M. J. Fadaee, and R. Tabatabaei. "A new formulation based upon trigonometric function for finite circular arch elements." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 8 (August 1, 2008): 1371–80. http://dx.doi.org/10.1243/09544062jmes487.

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In this paper, the formulation of the curved beam element by trigonometric functions for the curvature, which is an alternative to the displacement function is presented. Trigonometric function is chosen for the curvature to avoid the shear and membrane locking phenomena. In the developed formulation, the force—curvature relationships in polar coordinate system have been obtained first; then the curvature of the element has been assumed to have a trigonometric function form; and the radial and tangential displacements, and rotation of the cross-section have been found to be a function of the curvature. Moreover, the relationship between the nodal curvatures and the nodal deformations has been calculated and used for determining the deformations in terms of curvature at an arbitrary point. The total potential energy has been calculated accounting for bending, shear, and tangential deformations. Invoking the stationary condition of the system, the force—deformation relationship for the element has been obtained. Using this relationship, the stiffness matrix and the equivalent fixed loads applying at the nodes have been computed. In such an equilibrium equation, the locking phenomenon is eliminated. The formulation is applied to six examples to verify its capabilities. The results demonstrate that the presented element is capable of representing the behaviour of the curved beam with adequate accuracy and efficiency as compared with the previous methods.

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15

Cardoso, Rui P. R., Jeong Whan Yoon, and Robertt A. Fontes Valente. "A new approach to reduce membrane and transverse shear locking for one-point quadrature shell elements: linear formulation." International Journal for Numerical Methods in Engineering 66, no. 2 (2006): 214–49. http://dx.doi.org/10.1002/nme.1548.

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16

Marinković, Dragan, Gil Rama, and Manfred Zehn. "ABAQUS IMPLEMENTATION OF A COROTATIONAL PIEZOELECTRIC 3-NODE SHELL ELEMENT WITH DRILLING DEGREE OF FREEDOM." Facta Universitatis, Series: Mechanical Engineering 17, no. 2 (July 26, 2019): 269. http://dx.doi.org/10.22190/fume190530030m.

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Integration of classical, passive structures and active elements based on multi-functional materials resulted in a novel structural concept denoted as active structures. The new structural systems are characterized by self-sensing and actuation. Coupling the two distinctive features by means of a controller enables a number of exquisite functionalities such as vibration suppression, noise attenuation, shape control, structural health monitoring, etc. Reliable, accurate and highly efficient modeling tools are an important ingredient of the active structure design. This paper addresses the Abaqus implementation of a recently developed piezoelectric 3-node shell element. The element uses co-rotational formulation to cover geometric nonlinearities. Special techniques are used to address the issues originating from low-order interpolation functions. The discrete shear gap is used to resolve the shear locking, while the assumed natural deviatoric strain technique improves the membrane behavior. Examples are computed in Abaqus upon implementation of the developed element.

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17

Ghassemi, A., A. Shahidi, and M. Farzin. "A New Method for Analysing Large Elasto-Plastic Deformations of a Thin Cosserat Shell." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 10 (April 22, 2010): 2055–71. http://dx.doi.org/10.1243/09544062jmes1930.

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One of the best approaches for modelling the large deformation of shells is the Cosserat surface; however, the finite-element implementation of this model suffers from membrane and shear locking, especially for very thin shells. If the director vector is constrained to remain perpendicular to the mid-surface, during deformation, locking will be prevented. This constraint is in fact a limiting analysis of the Cosserat theory in which Kirchhoff's hypothesis is enforced. This has been considered for the first time. Simo's plastic approach is modified to implement the constrained director. This model includes both kinematic and isotropic hardening behaviours. A consistent elasto-plastic tangent modular matrix is extracted. Numerical solution is performed by interpolation of displacement on the whole domain, and a hierarchical finite-element scheme is developed. The principle of virtual work is used to obtain the weak form of the governing differential equations and the material and geometric stiffness matrices are derived through a linearization process. The validity and the accuracy of the method are illustrated by numerical examples.

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18

Shi, G., Y. Liu, and X. Wang. "Accurate, Efficient, and Robust Q4-Like Membrane Elements Formulated in Cartesian Coordinates Using the Quasi-Conforming Element Technique." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/198390.

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By using the quasi-conforming element technique, two four-node quadrilateral membrane elements with 2 degrees of freedom at each node (Q4-like membrane element) are formulated in rectangular Cartesian coordinates. One of the four-node quadrilateral membrane elements is based on the assumed strain field with only five independent strain parameters and accounting for the Poisson effect explicitly. There are no independent internal parameters and numerical integration involved in the evaluation of the strain parameters in these four-node quadrilateral membrane elements, and their element stiffness matrices are computed explicitly in Cartesian coordinates. Consequently, the formulation of these four-node quadrilateral membrane elements is extremely simple, and the resulting elements are very computationally efficient. These two quasi-conforming quadrilateral membrane elements pass the patch test and are free from shear locking and insensitive to the element distortion in the range of practical application. The numerical result comparison with other four-node quadrilateral membrane elements, including Q4-like plane elements with drilling degrees of freedom and the Q6-type isoparametric elements with very complicated nonconforming modes, shows that the present quasi-conforming quadrilateral membrane elements are not only reliable and robust, but also very accurate in both displacement and stress evaluations in the analysis of practical plane elasticity problems.

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19

SAYAKOUMMANE, VILAYSAK, and WORSAK KANOK-NUKULCHAI. "A MESHLESS ANALYSIS OF SHELLS BASED ON MOVING KRIGING INTERPOLATION." International Journal of Computational Methods 04, no. 04 (December 2007): 543–65. http://dx.doi.org/10.1142/s0219876207000935.

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An Element Free Galerkin Method (EFGM) for the analysis of degenerated shell structures is presented. The method is based on the Moving Kriging (MK) Interpolation function. The properties of the interpolation function possess the Kronecker delta property. With the MK Interpolation function no additional treatment required at the boundary conditions compared with that of using Moving Least Square (MLS) approximation. This deficiency of MLS at boundary condition has been definitely eradicated. The membrane and shear locking in the numerical analysis for degenerated shell problems has been alleviated by using higher order and removed by using quartic order of polynomials. Numerical benchmark examples for shell structures are presented to validate the proposed approach.

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20

WANG, DONGDONG, and YUE SUN. "A GALERKIN MESHFREE METHOD WITH STABILIZED CONFORMING NODAL INTEGRATION FOR GEOMETRICALLY NONLINEAR ANALYSIS OF SHEAR DEFORMABLE PLATES." International Journal of Computational Methods 08, no. 04 (November 20, 2011): 685–703. http://dx.doi.org/10.1142/s0219876211002769.

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A Galerkin meshfree approach formulated within the framework of stabilized conforming nodal integration (SCNI) is presented for geometrically nonlinear analysis of large deflection shear deformable plates. This method is based upon a Lagrangian curvature smoothing in which the smoothed curvature is constructed within a nodal representative domain on the initial configuration. It is shown that the Lagrangian smoothed nodal gradients of the meshfree shape function is capable of exactly representing arbitrary constant curvature fields in the discrete sense of nodal integration. The consistent linearization is performed on the weak form of large deflection plate in the context of the total Lagrangian description. Subsequently, the discrete incremental equations are obtained by the method of SCNI in which to relieve the locking as well as ensure the stability of the present scheme, the bending contribution is evaluated using the smoothed nodal gradients, while the membrane and shear contributions are computed with the direct nodal gradients. The effectiveness of the present method is thoroughly demonstrated through several numerical examples.

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21

Rezaiee-Pajand, Mohammad, Nima Gharaei-Moghaddam, and Mohammadreza Ramezani. "Higher-order assumed strain plane element immune to mesh distortion." Engineering Computations 37, no. 9 (April 13, 2020): 2957–81. http://dx.doi.org/10.1108/ec-09-2019-0422.

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Purpose This paper aims to propose a new robust membrane finite element for the analysis of plane problems. The suggested element has triangular geometry. Four nodes and 11 degrees of freedom (DOF) are considered for the element. Each of the three vertex nodes has three DOF, two displacements and one drilling. The fourth node that is located inside the element has only two translational DOF. Design/methodology/approach The suggested formulation is based on the assumed strain method and satisfies both compatibility and equilibrium conditions within each element. This establishment results in higher insensitivity to the mesh distortion. Enforcement of the equilibrium condition to the assumed strain field leads to considerably high accuracy of the developed formulation. Findings To show the merits of the suggested plane element, its different properties, including insensitivity to mesh distortion, particularly under transverse shear forces, immunities to the various locking phenomena and convergence of the element are studied. The obtained results demonstrate the superiority of the suggested element compared with many of the available robust membrane elements. Originality/value According to the attained results, the proposed element performs better than the well-known displacement-based elements such as linear strain triangular element, Q4 and Q8 and even is comparable with robust modified membrane elements.

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22

Wang, Yu, and Guangyu Shi. "Simple and Accurate Eight-Node and Six-Node Solid-Shell Elements with Explicit Element Stiffness Matrix Based on Quasi-Conforming Element Technique." International Journal of Applied Mechanics 09, no. 01 (January 2017): 1750012. http://dx.doi.org/10.1142/s1758825117500120.

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Based on the quasi-conforming (QC) element technique, accurate and reliable eight-node and six-node solid-shell elements are presented in this paper. These QC solid-shell elements can alleviate shear and Poisson thickness locking by appropriately interpolating the strain fields over the element domain, and they are completely free from hourglass modes by ensuring the rank sufficiency of the element stiffness matrix a priori. Furthermore, the element stiffness matrices of the present elements are evaluated explicitly rather than resorting to the numerical integration, which leads to a high computational efficiency. The QC solid-shell elements with the properly interpolated element strain fields can rigorously pass both membrane and bending patch tests. The popular benchmark problems are used to evaluate the performance of the QC solid-shell elements. The numerical results show that the present QC solid-shell elements yield not only accurate displacements but also good stress results for all the stress components. Particularly, the present QC solid-shell elements are capable of giving quite accurate results even with very coarse mesh.

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23

Li, Z. X., T. Zheng, L. Vu-Quoc, and B. A. Izzuddin. "A 4-Node Co-Rotational Quadrilateral Composite Shell Element." International Journal of Structural Stability and Dynamics 16, no. 09 (November 2016): 1550053. http://dx.doi.org/10.1142/s0219455415500534.

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A 4-node co-rotational quadrilateral composite shell element is presented. The local coordinate system of the element is a co-rotational framework defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product. Thus, the element rigid-body rotations are excluded in calculating the local nodal variables from the global nodal variables. Compared with other existing co-rotational finite-element formulations, the present element has two features: (i) The two smallest components of the mid-surface normal vector at each node are defined as the rotational variables, leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure; (ii) both element tangent stiffness matrices in the local and global coordinate systems are symmetric owing to the commutativity of the nodal variables in calculating the second derivatives of strain energy with respect to the local nodal variables and, through chain differentiation with respect to the global nodal variables. In the modeling of composite structures, the first-order shear deformable laminated plate theory is adopted in the local element formulation, where both the thickness deformation and the normal stress in the direction of the shell thickness are ignored, and an assumed strain method is employed to alleviate the membrane and shear locking phenomena. Several examples involving composite plates and shells with large displacements and large rotations are presented to testify to the reliability and convergence of the present formulation.

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24

Cinefra, Maria, and Erasmo Carrera. "Shell Finite Elements for the Analysis of Multifield Problems in Multilayered Composite Structures." Applied Mechanics and Materials 828 (March 2016): 215–36. http://dx.doi.org/10.4028/www.scientific.net/amm.828.215.

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This paper deals with the analysis of layered structures under thermal and electro-mechanical loads. Constitutive equations for multifield are considered and the Principle of Virtual Displacements (PVD) is employed to derive the governing equations. The MITC9 shell finite element based on the Carrera's Unified Formulation (CUF) has been applied for the analysis. The models grouped in the CUF have variable through-the-thickness kinematic and they provide an accurate distribution of displacements and stresses along the thickness of the laminate. The shell element has nine nodes and the Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomenon. The finite element analysis of multilayered plates and shells has been addressed. Variable kinematics, as well as layer-wise and equivalent single layer descriptions, have been considered for the presented FEs, according to CUF. A few problems are analyzed to show the effectiveness of the proposed approach. Various laminations, thickness ratios and curvature ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in literature and the analytical solutions obtained using the CUF and the Navier's method.

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Pham, Quoc-Hoa, The-Van Tran, Tien-Dat Pham, and Duc-Huynh Phan. "An Edge-Based Smoothed MITC3 (ES-MITC3) Shell Finite Element in Laminated Composite Shell Structures Analysis." International Journal of Computational Methods 15, no. 07 (October 12, 2018): 1850060. http://dx.doi.org/10.1142/s0219876218500603.

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This paper proposes an improvement of the MITC3 shell finite element to analyze of laminated composite shell structures. In order to enhance the accuracy and convergence of MITC3 element, an edge-based smoothed finite element method (ES-FEM) is applied to the derivation of the membrane, bending and shear stiffness terms of the MITC3 element, named ES-MICT3. In the ES-FEM, the smoothed strain is calculated in the domain that constructed by two adjacent MITC3 triangular elements sharing an edge. On a curved geometry of shell models, two adjacent MITC3 triangular elements may not be placed on the same plane. In this case, the edge-based smoothed strain can be performed on the virtual plane based on strain transformation matrices between the global coordinate and this virtual coordinate. Furthermore, a simple modification coefficient is chosen to be [Formula: see text] times the maximum diagonal value of the element stiffness matrix at the zero drilling degree of freedom to avoid the drill rotation locking when all elements meeting at a node are coplanar. The numerical examples demonstrated that the proposed method achieves the high accuracy in comparison to others existing elements in the literature.

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26

Ton-That, Hoang Lan, Hieu Nguyen-Van, and Thanh Chau-Dinh. "An Improved Four-Node Element for Analysis of Composite Plate/Shell Structures Based on Twice Interpolation Strategy." International Journal of Computational Methods 17, no. 06 (April 4, 2019): 1950020. http://dx.doi.org/10.1142/s0219876219500208.

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This paper deals with numerical linear analyses of laminated composite plate/shell structures. The method is based on a four-node quadrilateral element, namely, SQ4T, within the framework of the first-order shear deformation theory (FSDT). This element is established by incorporating the twice interpolation strategy (TIS) into a traditional four-node finite element to build the membrane, bending and shear stiffness matrices. Many desirable characteristics of this efficient numerical method are shown as continuous nodal gradients, higher-order polynomial basis, no increase in number of the degree of freedom of the system. The performance of the proposed element is validated and demonstrated through several numerical benchmark problems. Convergence studies and comparison with other existing solutions in the literature suggest that the present element is efficient, accurate and free of lockings.

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27

Park, Weon-Tae. "Structural Stability and Dynamics of FGM Plates Using an Improved 8-ANS Finite Element." Advances in Materials Science and Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/2821473.

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I investigate the vibration and buckling analysis of functionally graded material (FGM) structures, using a modified 8-node shell element. The properties of FGM vary continuously through the thickness direction according to the volume fraction of constituents defined by sigmoid function. The modified 8-ANS shell element has been employed to study the effect of power law index on dynamic analysis of FGM plates with various boundary conditions and buckling analysis under combined loads, and interaction curves of FGM plates are carried out. To overcome shear and membrane locking problems, the assumed natural strain method is employed. In order to validate and compare the finite element numerical solutions, the reference results of plates based on Navier’s method, the series solutions of sigmoid FGM (S-FGM) plates are compared. Results of the present study show good agreement with the reference results. The solutions of vibration and buckling analysis are numerically illustrated in a number of tables and figures to show the influence of power law index, side-to-thickness ratio, aspect ratio, types of loads, and boundary conditions in FGM structures. This work is relevant to the simulation of wing surfaces, aircrafts, and box structures under various boundary conditions and loadings.

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28

Becker, Christoph, Kerim Isik, Ahmet Bayraktar, Sami Chatti, Matthias Hermes, Celal Soyarslan, and A. Erman Tekkaya. "Numerical Investigation of the Incremental Tube Forming Process." Key Engineering Materials 554-557 (June 2013): 664–70. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.664.

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As a response to the recent years’ growing demand for innovation in manufacturing processes towards lightweight design in several industrial sectors, a new process, called Incremental Tube Forming (ITF), and a corresponding machine layout have been developed. ITF is a process to manufacture bent tubes with varying cross-sections. During ITF a tube is clamped in a feeding device, which transports the tube through a spinning tool, where the diameter reduction takes place. This stage is followed by a superposed bending process without suppressing continuous feeding. This combination leads to various advantages such as improved tool life with reduced tool forces and improved product accuracy (e.g. springback behavior), as it is shown in various experimental works. This paper presents a complementary numerical treatment of the process using FEA. For this purpose, a 3D model is constructed using ABAQUS/Explicit, where the tube is modeled with conventional shell elements with uniformly reduced integration to avoid shear and membrane locking (S4R), whereas the spinning rolls are modeled as discrete rigid. With this model, the influences of process parameters, such as diameter reduction ratio and tool geometry, are investigated. This helps not only to gain a deeper understanding of the process but also to interpret already gathered experimental data with better precision and, thus establishing a basis for further improvement and optimization of this fairly new process.

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29

Kulikov, G. M., and S. V. Plotnikova. "Exact geometry SaS solid-shell element for 3D stress analysis of FGM piezoelectric structures." Curved and Layered Structures 5, no. 1 (June 1, 2018): 116–35. http://dx.doi.org/10.1515/cls-2018-0009.

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Abstract A hybrid-mixed functionally graded material (FGM) piezoelectric four-node solid-shell element through the sampling surfaces (SaS) method is proposed. The SaS formulation is based on choosing inside the shell N SaS parallel to the middle surface in order to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. Such choice of unknowns with the use of Lagrange polynomials of degree N-1 in through-thickness interpolations of the displacements, strains, electric potential, electric field and material properties leads to a robust FGM piezoelectric shell formulation. The inner SaS are located at Chebyshev polynomial nodes that make it possible to minimize uniformly the error due to Lagrange interpolation. To implement the effective analytical integration throughout the element, the extended assumed natural strain (ANS) method is employed. As a result, the piezoelectric four-node solid-shell element exhibits a superior performance in the case of coarse meshes. To circumvent shear and membrane locking, the hybrid stress-strain solid-shell formulation via the Hu-Washizu variational principle is employed. The developed solid-shell element could be useful for the 3D stress analysis of FGMstructures because the SaS method allows obtaining the solutions with a prescribed accuracy, which asymptotically approach the exact solutions of electroelasticity as the number of SaS tends to infinity.

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30

Winkler, Robert. "Comments on Membrane Locking." PAMM 10, no. 1 (November 16, 2010): 229–30. http://dx.doi.org/10.1002/pamm.201010107.

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31

Wolthuizen, D. J., R. H. W. Ten Thije, and R. Akkerman. "Simple Tests as Critical Indicator of Intra-Ply Shear Locking." Key Engineering Materials 554-557 (June 2013): 512–20. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.512.

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Standard finite elements can exhibit the numerical artifact of intra-plyshear locking during forming simulations. The displacement fields of elementsare piecewise continuous and cannot correctly capturediscontinuities in the shear field. This shear locking is illustrated insimulations of bias-extension experiments with an unaligned mesh. Two simpletests were developed as a critical indicator of intra-ply shear locking intriangular elements. A single-element-test shows the origin of the locking anda pull-out test indicates locking caused by small misalignments of theelements.

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32

Wolthuizen, D. J., and R. Akkerman. "Locking and Enrichment Strategies." Key Engineering Materials 651-653 (July 2015): 452–57. http://dx.doi.org/10.4028/www.scientific.net/kem.651-653.452.

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A short overview of different locking mechanisms is presented, in which the more recent locking phenomenon tension locking is placed. Tension locking is found during composite forming simulations and occurs when the element edges are unaligned with the fiber directions. Discontinuities in composite forming simulations show similarities with other weak discontinuities such as material interfaces and shear bands found during shear localization. Two enrichment strategies are explored to resolve tension locking in linear triangular elements.

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33

Cho, J. Y., and S. N. Atluri. "Analysis of shear flexible beams, using the meshless local Petrov‐Galerkin method, based on a locking‐free formulation." Engineering Computations 18, no. 1/2 (February 1, 2001): 215–40. http://dx.doi.org/10.1108/02644400110365888.

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The problems of shear flexible beams are analyzed by the MLPG method based on a locking‐free weak formulation. In order for the weak formulation to be locking‐free, the numerical characteristics of the variational functional for a shear flexible beam, in the thin beam limit, are discussed. Based on these discussions a locking‐free local symmetric weak form is derived by changing the set of two dependent variables in governing equations from that of transverse displacement and total rotation to the set of transverse displacement and transverse shear strain. For the interpolation of the chosen set of dependent variables (i.e. transverse displacement and transverse shear strain) in the locking‐free local symmetric weak form, the recently proposed generalized moving least squares (GMLS) interpolation scheme is utilized, in order to introduce the derivative of the transverse displacement as an additional nodal degree of freedom, independent of the nodal transverse displacement. Through numerical examples, convergence tests are performed. To identify the locking‐free nature of the proposed method, problems of shear flexible beams in the thick beam limit and in the thin beam limit are analyzed, and the numerical results are compared with analytical solutions. The potential of using the truly meshless local Petrov‐Galerkin (MLPG) method is established as a new paradigm in totally locking‐free computational analyses of shear flexible plates and shells.

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Neunteufel, Michael, and Joachim Schöberl. "Avoiding membrane locking with Regge interpolation." Computer Methods in Applied Mechanics and Engineering 373 (January 2021): 113524. http://dx.doi.org/10.1016/j.cma.2020.113524.

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35

Reddy, J. N. "On locking-free shear deformable beam finite elements." Computer Methods in Applied Mechanics and Engineering 149, no. 1-4 (October 1997): 113–32. http://dx.doi.org/10.1016/s0045-7825(97)00075-3.

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Kanok-Nukulchai, W., W. J. Barry, and K. Saran-Yasoontorn. "Meshless formulation for shear-locking free bending elements." Structural Engineering and Mechanics 11, no. 2 (February 25, 2001): 123–32. http://dx.doi.org/10.12989/sem.2001.11.2.123.

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37

Ozdemir, Y. I., and Y. Ayvaz. "Is it shear locking or mesh refinement problem?" Structural Engineering and Mechanics 50, no. 2 (April 25, 2014): 181–99. http://dx.doi.org/10.12989/sem.2014.50.2.181.

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38

Baier-Saip, J. A., P. A. Baier, A. R. de Faria, J. C. Oliveira, and H. Baier. "Shear locking in one-dimensional finite element methods." European Journal of Mechanics - A/Solids 79 (January 2020): 103871. http://dx.doi.org/10.1016/j.euromechsol.2019.103871.

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39

Xia, Ping, and Ke Xiang Wei. "Shear Locking Analysis of Plate Bending by Using Meshless Local Radial Point Interpolation Method." Applied Mechanics and Materials 166-169 (May 2012): 2867–70. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.2867.

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The shape function of the meshless local radial point interpolation method is constructed by using the radial basis functions and possesses Kronecker delta function properties. Therefore, the essential boundary conditions can be easily imposed. Causation of shear locking occur in plate bending is analyzed. Bending problems for plate with two sides simply supported, the other two sides clamped boundary conditions, are analyzed by the meshless local radial point interpolation method. The shear locking is easier avoided in the meshless method than in the finite element method, and the measure of avoiding the shear locking are presented.

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40

Kabir, Humayun R. H., and Abdullateef M. Al-Khaleefi. "Frequency Response of a Three-Node Finite Element for Thick and Thin Plates." Journal of Vibration and Control 8, no. 8 (August 2002): 1123–53. http://dx.doi.org/10.1177/107754602029584.

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A shear-locking free isoparametric three-node triangular finite element is presented to study the frequency response of moderately thick and thin plates. Reissner/Mindlin theory that incorporates shear deformation effects is included into the element formulation. A shear correction term is introduced in transverse shear strain components to avoid the shear-locking phenomenon. The element is developed with a full integration scheme, hence, the element remains kinematically stable. Natural frequencies and mode shapes are obtained and compared with the available analytical and finite element solutions.

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41

Hou-Cheng, Huang. "Membrane locking and assumed strain shell elements." Computers & Structures 27, no. 5 (1987): 671–77. http://dx.doi.org/10.1016/0045-7949(87)90083-6.

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42

Laulusa, A., and J. N. Reddy. "On shear and extensional locking in nonlinear composite beams." Engineering Structures 26, no. 2 (January 2004): 151–70. http://dx.doi.org/10.1016/s0141-0296(03)00175-5.

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43

Guo, Peijun, and Xubin Su. "Shear strength, interparticle locking, and dilatancy of granular materials." Canadian Geotechnical Journal 44, no. 5 (May 1, 2007): 579–91. http://dx.doi.org/10.1139/t07-010.

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The effect of particle angularity on the strength and dilation of granular materials is investigated through a series of laboratory tests on two materials, Ottawa standard sand (Sand O) and crushed limestone (Sand L), that are made up of rounded and angular particles, respectively. Triaxial tests on both materials at different confining pressures and initial void ratios show that particle angularity has a substantial effect on both the peak friction angle ϕp and the mobilized friction angle at the onset of dilation, ϕf. It is found that ϕf is smaller than the critical friction angle ϕcv for Ottawa sand; nevertheless ϕf is larger than ϕcv for Sand L owing to interparticle locking induced by particle angularity. The experimental results clearly show the contributions to shear resistance from both dilation and interlocking, with interlocking still largely existing at the peak stress ratio but not at the critical state. Suggestions are made to modify the stress–dilatancy formulations for sand to take into account the effect of interparticle locking associated with particle angularity.Key words: granular material, dilatancy, interlocking, and particle shape.

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44

Yuvakishore, Bheema, R. Yogeshwaran, and P. V. Jeyakathikeyan. "Shear locking reduction in family of plane quadrilateral elements." IOP Conference Series: Materials Science and Engineering 402 (September 20, 2018): 012074. http://dx.doi.org/10.1088/1757-899x/402/1/012074.

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45

Carpenter, Nicholas, Ted Belytschko, and Henryk Stolarski. "Locking and shear scaling factors in C° bending elements." Computers & Structures 22, no. 1 (January 1986): 39–52. http://dx.doi.org/10.1016/0045-7949(86)90083-0.

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46

Rakowski, J. "The interpretation of the shear locking in beam elements." Computers & Structures 37, no. 5 (January 1990): 769–76. http://dx.doi.org/10.1016/0045-7949(90)90106-c.

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47

Wong, F. T., Adam Sulistio, and Hidayat Syamsoeyadi. "Kriging-Based Timoshenko Beam Elements with the Discrete Shear Gap Technique." International Journal of Computational Methods 15, no. 07 (October 12, 2018): 1850064. http://dx.doi.org/10.1142/s0219876218500640.

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Kriging-based finite element method (K-FEM) is an enhancement of the FEM through the use of Kriging interpolation in place of the conventional polynomial interpolation. In this paper, the K-FEM is developed for static, free vibration, and buckling analyses of Timoshenko beams. The discrete shear gap technique is employed to eliminate shear locking. The numerical tests show that a Kriging-Based beam element with cubic basis and three element-layer domain of influencing nodes is free from shear locking. Exceptionally accurate displacements, bending moments, natural frequencies, and buckling loads and reasonably accurate shear force can be achieved using a relatively course mesh.

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48

Yu, Shu Qiang, Ming Zhang, and Lu Lu Fan. "A Universal Finite Element of Thick and Thin Plate without Shear Locking." Applied Mechanics and Materials 52-54 (March 2011): 1353–57. http://dx.doi.org/10.4028/www.scientific.net/amm.52-54.1353.

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In order to prevent shear locking, a method using theory of deep beam is proposed. A universal finite element for thick and thin plates is constructed. When the plate thickness approaches to the limit of thin plate, the universal element degenerates to the thin plate element automatically. As a results, the shear locking phenomenon will not appear. The computational results indicate that the current element has high-accuracy and good usefulness.

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Koschnick, Frank, Manfred Bischoff, Natalia Camprubí, and Kai-Uwe Bletzinger. "The discrete strain gap method and membrane locking." Computer Methods in Applied Mechanics and Engineering 194, no. 21-24 (June 2005): 2444–63. http://dx.doi.org/10.1016/j.cma.2004.07.040.

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Raveendranath, P., Gajbir Singh, and B. Pradhan. "A two-noded locking-free shear flexible curved beam element." International Journal for Numerical Methods in Engineering 44, no. 2 (January 20, 1999): 265–80. http://dx.doi.org/10.1002/(sici)1097-0207(19990120)44:2<265::aid-nme505>3.0.co;2-k.

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