Finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements

In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.

RATIONAL FINITE ELEMENT METHOD FOR ELASTIC BENDING OF REISSNER PLATES

In this paper; some deformation patterns defined by differential equations of the elastic system are introduced into the revised functional for the incompatible elements. And therefore the rational FEM, which is perfect combination of the analytic methods and numeric methods, has been presented. This new approach satisfies not only the mechanical requirement of the elements but also the geometric requirement of the complex structures. What's more the quadrilateral element obtained accordingly for the elastic bending of thick plates demonstrates such advantages as high precision for computation and availability of accurate integration for stiffness matrices.

Application of the quadrilateral area coordinate method:a new element for laminated composite plate bending problems

Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate （QAC） method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF （5-DOF per node） quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-rocessing procedure, which was firstly proposed by the authors, is employed again to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models.

B-Spline Wavelet on Interval Finite Element Method for Static and Vibration Analysis of Stiffened Flexible Thin Plate

A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.

Static and free vibration analyses of functionally graded porous variable-thickness plates using an edge-based smoothed finite element method

The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.

Force-Based Quadrilateral Plate Bending Element for Plate Using Large Increment Method

A force-based quadrilateral plate element( 4NQP13) for the analysis of the plate bending problems using large increment method( LIM) was proposed. The LIM, a force-based finite element method( FEM),has been successfully developed for the analysis of truss,beam,frame,and 2D continua problems. In these analyses,LIMcan provide more precise stress results and less computational time consumption compared with displacement-based FEM. The plate element was based on the Mindlin-Reissner plate theory which took into account the transverse shear effects.Numerical examples were presented to study its performance including accuracy and convergence behavior,and the results were compared with the results have been obtained from the displacementbased quadrilateral plate elements and the analytical solutions. The4NQP13 element can analyze the moderately thick plates and the thin plates using LIMand is free from spurious zero energy modes and free from shear locking for thin plate analysis.

Finite Element Analysis Study of Prototype of a Novel Intramedullary Injectable Bioresorbable Polymer Fixator versus a Volar Plate for Surgical Treatment of Distal Radius Fractures

Complications and shortcomings of volar plating, which is very widely used for surgical treatment of distal radius fractures, are well known. Thus, there is scope for alternative innovative surgical methods. In the present work, we used the finite element analysis method to compare the biomechanical performance of a model of a construct comprising a simulated distal radius fracture considered fixated using a notional intramedullary injectable bioresorbable polymer-bioresorbable balloon osteosynthesis system (“fixator”) versus using a commercially-available volar locking plate (VP). The biomechanical parameters determined were longitudinal stiffness and factor of safety under each of the applied loads.?For the fixator model, 1) each of the biomechanical parameters was markedly influenced by fracture gap fill ratio (FGFR) (defined as the proportion of the volume of the fracture gap that is considered occupied by the expanded polymer-filled balloon)?but not by modulus of elasticity assigned to the polymer;2) with FGFR = 100%, stiffness was comparable to that of the Ti-6Al-4V alloy VP construct model;and 3) stiffness was within the range of literature values for stiffness of constructs comprising simulated fractures in fresh cadaveric distal radii fixated using metal volar locking plate. These results suggest that the fixator may be an alternative modality to metal volar plating and, as such, deserves further evaluation.

A New Rectangular Finite Element Formulation Based on Higher Order Displacement Theory for Thick and Thin Composite and Sandwich Plates

A new displacement based higher order element has been formulated that is ideally suitable for shear deformable composite and sandwich plates. Suitable functions for displacements and rotations for each node have been selected so that the element shows rapid convergence, an excellent response against transverse shear loading and requires no shear correction factors. It is completely lock-free and behaves extremely well for thin to thick plates. To make the element rapidly convergent and to capture warping effects for composites, higher order displacement terms in the displacement kinematics have been considered for each node. The element has eleven degrees of freedom per node. Shear deformation has also been considered in the formulation by taking into account shear strains ( rxz and ryz) as nodal unknowns. The element is very simple to formulate and could be coded up in research software. A small Fortran code has been developed to implement the element and various examples of isotropic and composite plates have been analyzed to show the effectiveness of the element.

A Comparative Study of Stress Recovery Method and Error Estimation of Plate Bending Problem Using DKMQ Element

Recovery by Equilibrium in Patches (REP) is a recovery method introduced by B. Boroomand. This method is using patch as recovery media as is used by Superconvergent Patch Recovery (SPR) which is well known as a good recovery method. In this research, a numerical study of REP implementation is held to estimate error in finite element analysis using DKMQ element. The numerical study is performed with both uniform and adaptive h-type mesh refinement. The result is compared with three other recovery method, i.e. SPR method, averaging method, and projection method.

P-FEMOL ANALYSIS OF PLATE BENDING PROBLEMS

In this paper, the p- version of the finite element method of lines (FEMOL) for the analysis of the Mindlin-Reissner plate bending problems is presented and a class of p-FEMOL elements with polynomial degrees as high as nine is developed. Numerical examples given in this paper show tremendous performance of the present method: namely, rapid convergence rate, high accuracy for both displacements and stress resultants, removal of shear-locking trouble, capability of dealing with difficult problems such as the boundary layer behavior near a free edge and stress concentration around a hole.

A Finite Element Model of Locked Plating in Femoral Shaft Fractures

Introduction: The Locking Compression Plate (LCP) system is a versatile technology that can be used either through conventional compression plating techniques or as an internal fixator with locking head screws. There have been only a few biomechanical studies examining the role of locked screw configuration on construct stability with most recommendations based upon empirical evidence or data from compression plating. This study will attempt to determine how different locked screw configurations, fracture gaps (distance between bone fragments), and interface gaps (distance between plate and bone) will affect the peak stress(von Mises stress) experienced by the plate-screw construct and, thereby, look at ways to minimize the risk of hardware failure. Materials Methods: A finite element model (FEM) was developed of a transverse mid shaft femoral fracture bridged by an eight-hole titanium LCP. Seven different screw configurations were investigated. Three different fracture gaps and three different interface gaps were studied as well. Results: The 1368 configuration was found to experience the least peak stress of 2.10 GPa while the 2367, 2457, and all filled configurations were found to have the highest peak stress (25.29 GPa, 22.78 GPa, and 23.54 GPa, respectively). Peak stress increased when the interface gap increased. Peak stress also increased as the fracture gap increased, with the largest jump between the 1 mm and 2 mm gaps. Conclusions: Every fracture is unique, and has a vast amount of parameters that must be considered when the surgeon is developing a treatment plan. For transverse femoral shaft fractures, the results of this study suggest that a working length of 2 screw holes on either side of the fracture may also lead to lower peak stress. In addition, our results demonstrate that minimizing the fracture gap and interface gap will lead to decreased stress in the plate-screw construct.

SPECIAL HIGH-ORDER BENDING CRACK TIP FINITE ELEMENT FOR THE REISSNER PLATE

Based on the crack tip field expansion of the Reissner plate, a special high order bending crack tip element is developed, and the element stiffness matrix is given in the explicit form, which is especially convenient for engineering analyses. A numerical example is presented and compared with previous results to demonstrate the efficiency and accuracy of the special element.

TRAPEZOIDAL PLATE BENDING ELEMENT WITH DOUBLE SET PARAMETERS

Using double set parameter method, a 12-parameter trapezoidal plate bending element is presented. The first set of degrees of freedom, which make the element convergent, are the values at the four vertices and the middle points of the four sides together with the mean values of the outer normal derivatives along four sides. The second set of degree of freedom, which make the number of unknowns in the resulting discrete system small and computation convenient are values and the first derivatives at the four vertices of the element. The convergence of the element is proved.

A fiber-section model based Timoshenko beam element using shear-bending interdependent shape function

A fiber-section model based Timoshenko beam element is proposed in this study that is founded on the nonlinear analysis of frame elements considering axial, flexural, and shear deformations. This model is achieved using a shear-bending interdependent formulation （SBIF）. The shape function of the element is derived from the exact solution of the homogeneous form of the equilibrium equation for the Timoshenko deformation hypothesis.The proposed element is free from shear-locking. The sectional fiber model is constituted with a multi-axial plasticity material model, which is used to simulate the coupled shear-axial nonlinear behavior of each fiber. By imposing deformation compatibility conditions among the fibers, the sectional and elemental resisting forces are calculated. Since the SBIF shape functions are interactive with the shear-corrector factor for different shapes of sections, an iterative procedure is introduced in the nonlinear state determination of the proposed Timoshenko element. In addition, the proposed model tackles the geometric nonlinear problem by adopting a corotational coordinate transformation approach. The derivation procedure of the corotational algorithm of the SBIF Timoshenko element for nonlinear geometrical analysis is presented. Numerical examples confirm that the SBIF Timoshenko element with a fiber-section model has the same accuracy and robustness as the flexibility-based formulation. Finally, the SBIF Timoshenko element is extended and demonstratedin a three-dimensional numerical example.

A mechanical study of personalised Ti6Al4V tibial fracture fixation plates with grooved surface by finite element analysis

Low shape matching and high stress shielding rates between bone plate and human bone are not conducive to the primary healing of fracture.In this study,taking the fracture site of the lower one‐third of human tibia as an application case,six types of personalised Ti6Al4V tibial plates with grooved surface were designed and evaluated by reverse en-gineering and finite element analysis.The results showed that the grooved design can reduce the stress shielding rate of bone plate and promote the facture healing.Among the six types of bone plates,the‘OUT-MI’bone plate has the lowest stress shielding rate and the most uniform stress distribution.Meanwhile,with the increasing tibial load during the convalescence,the average stress and maximum axial displacement of the tibial fracture surface increased,which can effectively improve the bone regeneration in the tibial fracture area.Moreover,there was no significant difference in four-point bending performance between the‘OUT-MI’bone plate and the‘STR-BE’bone plate,indicating that the mechanical properties of this bone plate were reliable.The results provide a theoretical basis for the design of fracture fixation plates on clinical treatment.

A NOTE ON THE NONCONFORMING FINITE ELEMENTS FOR ELLIPTIC PROBLEMS

In this paper, a class of rectangular finite elements for 2m-th-oder elliptic boundary value problems in n-dimension （m, n ≥1） is proposed in a canonical fashion, which includes the （2m - 1）-th Hermite interpolation element （n = 1）, the n-linear finite element （m = 1） and the Adini element （m = 2）. A nonconforming triangular finite element for the plate bending problem, with convergent order （O（h2）, is also proposed.

Lateral load-carrying capacity analyses of composite shear walls with double steel plates and filled concrete with binding bars

A method is developed to predict the lateral load-carrying capacity of composite shear walls with double steel plates and filled concrete with binding bars(SCBs). Nonlinear finite element models of SCBs were established by using the finite element tool, Abaqus. Tie constraints were used to connect the binding bars and the steel plates. Surface-to-surface contact provided by the Abaqus was used to simulate the interaction between the steel plate and the core concrete. The established models could predict the lateral load-carrying capacity of SCBs with a reasonable degree of accuracy. A calculation method was developed by superposition principle to predict the lateral load-carrying capacity of SCBs for the engineering application. The concrete confined by steel plates and binding bars is under multi-axial compression; therefore, its shear strength was calculated by using the Guo-Wang concrete failure criterion. The shear strength of the steel plates of SCBs was calculated by using the von Mises yielding criterion without considering buckling. Results of the developed method are in good agreement with the testing and finite element results.

BENDING THEORIES FOR BEAMS AND PLATES WITH SINGLE GENERALIZED DISPLACEMENT

Classical bending theories for beams and plates can not be used for short, stubby beams and thick plates since transverse shearing effect is excluded, and ordinary theories with multiple generalized displacements can not be used for long, slender beams and thin plates since the innate relation between rotation angle and deflection is ignored. These two types of theories are not consistent due to the contradiction of dependence and independence of the rotation angle. Based on several basic assumptions, a new type of theories which not only include the transverse shearing effect is presented, but also the relation between potation angle and deflection is obtained. Analytical solutions of several simple beams are given. It has been testified by numerical examples that the new theories can be used for either long, slender beams and thin plates or short, stubby beams and thick plates.

LOCKING-FREE DEGENERATED ISOPARAMETRIC SHELL ELEMENT

An 8-noded locking-free degenerated isoparametric shell element is presented. A revised interpolation for shear strain terms was constructed in natural co-ordinate system such that all necessary modes (translation, rotation and constant curvature) are preserved, which can be used to eliminate shear locking. A revised interpolation for membrane strains was produced in the local Cartesian co-ordinate system to overcome membrane locking behavior. The new 8-noded element has the proper rank, with the requisite number of zero eigenvalues each associated with a rigid mode. The element does not exhibit membrane or shear locking for large span-thickness ratio. The element does not form element mechanisms or extra spurious zero energy modes. Therefore, it can be used for both thin and thick shells.

A NEW QUADRILATERAL THIN PLATE ELEMENT BASED ON THE MEMBRANE-PLATE SIMILARITY THEORY

A new effective path has been proposed to formulate thin plate element by using the similarity theory between plane elasticity and plate bending.Because of avoiding the difficulty of c(1)continuity,the construction of thin plate elements becomes easier.The similarity theory and its applications were discussed more deeply,and a new four nodes,sixteen D.O.F.(degree of freedom)thin plate element was presented on the base of the similarity theory.Numerical results for typical problems show that this new element can pass the patch test and has a very good convergence and a high precision.