Discrete Kirchhoff-Mindlin Research Articles

Static Convergence Behaviour of Discrete Kirchhoff-Mindlin Triangular Element on Rectangular Functionally Graded Material Plates

Rapid infrastructure development is consistent with the increase in innovation in structural elements. One of the main parameters in infrastructure development is materials. An advanced composite material called Functionally Graded Material (FGM) has been widely used. FGM is composed of the combination of two or more materials. FGM increases the bond strength between the layers compared to conventional composite materials, eliminating stress at the interface layers, and reducing cracks. However, further studies are required to understand the behaviour of the FGM plate. Finite element analysis (FEA) was considered to evaluate the convergence behaviour of the FGM plates. The Discrete Kirchhoff-Mindlin Triangular (DKMT) element is employed in the analysis. Studies regarding the FGM plates with the DKMT element were limited to square shapes and skew shapes. Thus, this study aims to study the convergence behaviour of the rectangular FGM plates composed of ceramic and metal. The FEA was carried out in different types of meshing, ratio a/h, ratio a/b, the power-law index, and boundary conditions. The analysis results indicate that the application of the DKMT element in analyzing the FGM plates gives good asymptotic and convergence behaviour. Thus, this method has proved reliable and sustainable.

Buckling analysis of square Functionally Graded Material (FGM) plate using Discrete Kirchhoff Mindlin Triangular (DKMT) element

This paper presents the convergence behavior of Discrete Kirchhoff Mindlin Triangular (DKMT) element in buckling analysis under uniaxial compression of square plate problems. The DKMT element has a good result for a thin plate and a thick plate. For the Functionally Graded Material (FGM) problem, the DKMT element is reformulated. FGM is a graded composite material that has high-temperature and structural flexibility resistance. The numerical results of mechanical buckling of square FGM plate under uniaxial compression using the DKMT element are reported. The critical buckling of the square FGM plate is compared to the reference existing solutions. The effects of parametric variation, such as the type of meshing, boundary conditions, power-law index, and ratio L/h are presented. The results show that the DKMT element gives good results on the buckling analysis of square FGM plate problems.

A new locking-free polygonal plate element for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields

A new n-noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The proposed element: (a) has proper rank; (b) passes patch test for both thin and thick plates; (c) is free from shear locking and (d) yields optimal convergence rates in L2-norm and H1-semi-norm. The accuracy and the convergence properties are demonstrated with a few benchmark examples.

FREE VIBRATION ANALYSIS OF CURVILINEARLY STIFFENED KIRCHHOFF-MINDLIN PLATES

Compared with traditional stiffened plates, curvilinearly stiffened plates can deliver the mechanical properties of materials more adequately. In mechanical analysis of stiffened thick plates, Reissner-Mindlin theory is usually adopted. However, difficulties are encountered in connection with shear locking when the plate thickness approaches zero. In order to avoid the above problem, the discrete Kirchhoff-Mindlin theory was investigated by employing the assumption of shear strain field. An efficient finite element approach for free vibration analysis of curvlinearly stiffened KirchhoffMindlin plates is presented in this paper. The discrete Kirchhoff-Mindlin triangular (DKMT) element and the Timoshenko curved beam element are employed for modeling the plate and the stiffeners, respectively. The finite element equation is established through the displacement interpolation function of plate and the displacement compatibility conditions at the plate-stiffener interfaces. In order to verify the efficiency and accuracy of the present method, linearly stiffened thin plate and curvilinearly stiffened thin and thick plates are used as numerical examples. The reasonable finite element mesh density is selected by convergence and accuracy analysis. The first 20 natural frequencies of the linearly stiffened plate are in good agreement with the literature. In the examples of the curvilinearly stiffened plate, the number of plate elements satisfying the convergence condition is 2469, while the number in Nastran model is 6243. The maximum error of the natural frequency between the present method and Nastran is 3.4%. Results show that present approach can guarantee the accuracy of calculation with less number of elements. The present method can be applied to the free vibration analysis of both stiffened thin and thick plates.

Development of the DKMT Element for Error Estimation in Composite Plate Structures

This paper presents an application of the Discrete Kirchhoff-Mindlin Triangular (DKMT) element for error estimation in composite structures. The DKMT element passed the patch tests and gave good results in many plate bending applications. The DKMT element formulation in composite application uses the same technique as the Discrete Kirchhoff-Mindlin Quadrilateral (DKMQ) composite introduced. The benchmark tests for composite plates have been analyzed, as validation, using the methods employed by Srinivas (1973) and Pagano (1970). The DKMT plate bending element gave a good performance in convergence tests and can be used as one of tools in analyzing composite structur es. Moreover, error estimation using various recovery methods such as Averaging, Projection and Superconvergent Patch Recovery (SPR) has been studied. All recovery methods used give similar results.

An efficient facet shell element for corotational nonlinear analysis of thin and moderately thick laminated composite structures

In the present work, an efficient facet shell element for the geometrically nonlinear analysis of laminated composite structures using the corotational approach is developed. The facet element is developed by combining the discrete Kirchhoff–Mindlin triangular bending element (DKMT), and the optimal membrane triangular element (OPT). The membrane-bending coupling effect of composite laminates is incorporated in the formulation, and inconsistent stress stiffness matrix is formulated. Using corotational formulation and the proposed facet element, some example laminated composite structures with geometric nonlinearity are analyzed, and the results are compared with those found using other facet elements.

The geometric stiffness of thick shell triangular finite elements for large rotations

AbstractThis paper is concerned with the development of the geometric stiffness matrix of thick shell finite elements for geometrically nonlinear analysis of the Newton type. A linear shell element that is comprised of the constant stress triangular membrane element and the triangular discrete Kirchhoff Mindlin theory (DKMT) plate element is ‘upgraded’ to become a geometrically nonlinear thick shell finite element. Perturbation methods are used to derive the geometric stiffness matrix from the gradient, in global coordinates, of the nodal force vector when stresses are kept fixed. The present approach follows earlier works associated with trusses, space frames and thin shells. It has the advantage of explicitness and clear physical insight. A special procedure, tailored to triangular elements is used to isolate pure rotations to enable stress recovery via linear elastic constitutive relations. Several examples are solved. The results compare well with those available in the literature. Copyright © 2005 John Wiley & Sons, Ltd.

A new triangular stiffened plate element for laminate analysis

A new stiffened plate element for the analysis of laminated stiffened plates has been presented. The basic plate element is a combination of Allman's plane stress triangular element and discrete Kirchhoff–Mindlin plate bending element. The stiffened plate element has been developed to include the effects of transverse shear. The element can accommodate any number of arbitrarily oriented stiffeners and is completely free from the usual constraints on the mesh division of the plates. The element has no problems associated with shear locking — a phenomenon usually encountered in isoparametric elements. Static and free vibration analyses of laminated stiffened plates have been carried out with this element and the results are compared with those published.

A new finite element for buckling analysis of laminated stiffened plates

A new stiffened plate element for stability analysis of laminated stiffened plates has been presented. The basic plate element is a combination of Allman's plane stress triangular element and a Discrete Kirchhoff–Mindlin plate bending element. The element includes transverse shear effects. The model accommodates any number of arbitrarily oriented stiffeners within the plate element and eliminates constraints on the mesh division of the plate. The element has no problem associated with shear locking – a phenomenon usually encountered in isoparametric elements. The stability analysis of laminated stiffened plates has been carried out under different loading conditions with the present element.