• Structural Engineering and Mechanics
• /
• v.5 no.4
• /
• pp.471-490
• /
• 1997

In this paper, the classical Irons' patch tests which have been generally accepted for the convergence proof of a finite element are performed for Mindlin plate bending elements with a special emphasis on the nonconforming elements. The elements considered are 4-node and 8-node quadrilateral isoparametric elements which have been dominantly used for the analyses of plate bending problems. It was recognized from the patch tests that some nonconforming Mindlin plate elements pass all the cases of patch tests even though nonconforming elements do not preserve conformity. Then, the clues for the Mindlin plate element to pass the Irons' patch tests are investigated. Also, the convergent characteristics of some nonconforming Mindlin plate elements that do not pass the Irons' patch tests are examined by weak patch tests. The convergence tests are performed on the benchmark numerical problems for both nonconforming elements which pass the patch tests and which do not. Some conclusions on the relationship between the patch test and convergence of nonconforming Mindlin plate elements are drawn.

• Computational Structural Engineering
• /
• v.3 no.4
• /
• pp.91-104
• /
• 1990

Static performance of quadrilateral plate elements was compared through numerical experiments. Sixteen plate elements were selected for comparison from the literature, which were displacement elements, equilibrium elements, mixed elements or hybrid elements based on the Kirchhoff theory or the Mindlin theory. Thin plate bending problems, such as square plate problems, rhombic plate problems, circular plate problems and cantilevered plate problems, were modeled by various meshes and solved under various kinds of boundary conditions. Kirchhoff elements were not so good as Mindlin elements in view of efficiency and convergence. Hinton's elements resulted in the best results for the problems considered with respect to efficiency, convergence and reliability but in some problems they also resulted in more or less inaccurate solutions.

• Structural Engineering and Mechanics
• /
• v.5 no.6
• /
• pp.853-865
• /
• 1997

The design of robust plate and shell elements has been a very challenging area for several decades. The main difficulty has been the shear locking phenomenon in plate elements and the shear and membrane locking phenomena together in the shell elements. Among the various artifices or devices which are used to develop elements free of these problems is the field-consistency approach. In this paper this approach is reviewed, It turns out that not only Mindlin type elements but also elements based on higher-order theories could be developed using the technique.

• Structural Engineering and Mechanics
• /
• v.19 no.3
• /
• pp.297-320
• /
• 2005

In recent years the pure displacement formulation for plate elements has not been as popular as other formulations. We revisit the pure displacement formulation for shear-deformable plate elements and propose a family of N-node, displacement-compatible, fully-integrated, pure-displacement, triangular, Mindlin plate elements, MIN-N. The development has been motivated by the relative simplicity of the pure displacement formulation and by the success of the existing 3-node plate element, MIN3. The formulation of MIN3 is generalized to obtain the MIN-N family, which possesses complete, fully compatible kinematic fields, in which the interpolation functions for transverse displacement are one degree higher than those for rotations. General element-level formulas for the thin-limit Kirchhoff constraints are developed. The 6-node, 18 degree-of-freedom element MIN6, with cubic displacement and quadratic rotations, is implemented and tested extensively. Numerical results show that MIN6 exhibits good performance for both static and dynamic analyses in the linear, elastic regime. The results illustrate that the fully-integrated MIN6 element has excellent performance in the thin limit, even for coarse meshes, and that it does not require shear relaxation.

• Structural Engineering and Mechanics
• /
• v.21 no.4
• /
• pp.407-422
• /
• 2005

Plate elements in fully profiled sandwich panels are generally subjected to local buckling failure modes and this behaviour is treated in design by using the conventional effective width method for plates with a width to thickness (b/t) ratio less than 100. If the plate elements are very slender (b/t > 1000), the panel failure is governed by wrinkling instead of local buckling and the strength is determined by the flexural wrinkling formula. The plate elements in fully profiled sandwich panels do not fail by wrinkling as their b/t ratio is generally in the range of 100 to 600. For this plate slenderness region, it was found that the current effective width formula overestimates the strength of the fully profiled sandwich panels whereas the wrinkling formula underestimates it. Hence a new effective width design equation has been developed for practical plate slenderness values. However, no guidelines exist to identify the plate slenderness (b/t) limits defining the local buckling, wrinkling and the intermediate regions so that appropriate design rules can be used based on plate slenderness ratios. A research study was therefore conducted using experimental and numerical studies to investigate the effect of plate slenderness ratio on the ultimate strength behaviour of foam supported steel plate elements. This paper presents the details of the study and the results.

• Structural Engineering and Mechanics
• /
• v.69 no.5
• /
• pp.527-536
• /
• 2019

This paper will compare $T3{\gamma}_s$ and MITC3 elements, both these two elements are three-node triangular plate bending elements with three degrees of freedom per node. The formulation of the $T3{\gamma}_s$ and MITC3 elements is rather simple and has already been widely used. This paper will prove that the shear strain formulation of these two elements is identical even though they are obtained from two different methods. A single element is used to test the formulation of shear strain matrices. Numerical tests for circular plate cases compared with the exact solutions and with DKMT element will complete this review to verify the performances and show the convergence of these two elements.

• Journal of Advanced Marine Engineering and Technology
• /
• v.26 no.3
• /
• pp.344-352
• /
• 2002

In the analysis of the 3 dimensional plate structures by the finite element method, the triangular elements are generally used for the global stiffness matrix of the analyzed system. But the triangular elements of the plates have some problems in the process of formulation and in the precision of analysis. The formulation of the finite element method to analyze 3 dimensional plate structures using quadrilateral elements is presented in this paper. The degree of freedom off nodal point is 6, that is, the displacements in the direction off-y-z is and the rotations about x-y-z axis and then the degree of freedom off element is 24. For the comparison of the analysis using triangular elements and quadrilateral elements, the rectangular plates subjected to the uniform load and a concentrated load on the centroid of the plate, for which the theoretical solutions have been obtained, are analyzed. The calculated deflections of the rectangular plates using the finite element method by the triangular elements and the quadrilateral elements are also compared with the deflections of the plates calculated by theoretical solutions. The defections of the rectangular plates calculated by the finite element method using the quadrilateral elements are closer to the theoretical solutions than the defections calculated by the finite element method using the triangular elements. The deflection of the centroid of plate, calculated by the finite element method, converges to that of theoretical solution as the number of elements is increased. This convergence is much more rapid for the case of using the quakrilateral elements than fir the case of using triangular elements.

• Structural Engineering and Mechanics
• /
• v.59 no.6
• /
• pp.1071-1094
• /
• 2016

We employ the so-called problem-dependent linked interpolation concept to develop two cubic 4-node quadrilateral plate finite elements with 12 external degrees of freedom that pass the constant bending patch test for arbitrary node positions of which the second element has five additional internal degrees of freedom to get polynomial completeness of the cubic form. The new elements are compared to the existing linked-interpolation quadratic and nine-node cubic elements presented by the author earlier and to the other elements from literature that use the cubic linked interpolation by testing them on several benchmark examples.

• Structural Engineering and Mechanics
• /
• v.7 no.4
• /
• pp.377-386
• /
• 1999

The stress distribution in a symmetrically laminated composite plate subjected to in-plane compression are evaluated using finite element analysis. Six different finite element models are created for the study of stresses in the plate after buckling. Two finite element modelling approaches are adopted to obtain the stress distribution. The first approach starts with a full model of shell elements from which sub-models of solid elements are spin-off The second approach adopts a full model of solid elements at the beginning from which sub-models of solid elements are created. All sub-models have either 1-element thickness or 14-element thickness. Both techniques show high interlaminar direct and shear stresses at the free edges. The study also provides vital information of the distribution of all components of stresses along the unloaded edges in length direction and also in the thickness direction of the plate.

• Structural Engineering and Mechanics
• /
• v.19 no.6
• /
• pp.619-637
• /
• 2005

The objective of this research was to determine the Vlasov soil parameters for quadratically varying elasticity modulus $E_s$(z) of the compressible soil continuum and discuss the interaction affect between two close plates. Interaction problem carried on for uniformly distributed load carrying plates. Plate region was simulated by Kirchhoff plate theory based (mixed or displacement type) 2D elements and the foundation continuum was simulated by displacement type 2D elements. At the contact region, plate and foundation elements were geometrically coupled with each other. In this study the necessary formulas for the Vlasov parameters were derived when Young's modulus of the soil continuum was varying as a quadratic function of z-coordinate through the depth of the foundation. In the examples, first the elements and the iterative FE algorithm was verified and later the results of quadratic variation of $E_s$(z) were compared with the previous examples in order to discuss the general behavior. As a final example two plates close to each other resting on elastic foundation were handled to see their interaction influences on the Vlasov foundation parameters. Original examples were solved using both mixed and displacement type plate elements in order to confirm the results.