• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1992.10a
• /
• pp.39-44
• /
• 1992

This paper is concerned with formulations of the hierarchical $C^{o}$-plate element on the basis of Reissner-Mindlin plate theory. On reason for the development of the aforementioned element is that it is still difficult to construct elements based on h-version concepts which are accurate and stable against the shear locking effects. An adaptive mesh refinement and selective p-distribution of the polynomial degree using hp-version of the finite element method we proposed to verify the superior convergence and algorithmic efficiency with the help of the clamped L-shaped plate problems.s.

• Structural Engineering and Mechanics
• /
• v.20 no.4
• /
• pp.477-493
• /
• 2005

In case of Mindlin plate, not only the bending deformation but also the shear behavior is allowed. While the bending and shear stiffness are given in the same order in terms of elastic modulus, they are in different order in case of plate thickness. Accordingly, bending and shear contributions have to be dealt with independently if the stochastic finite element analysis is performed on the Mindlin plate taking into account of the uncertain plate thickness. In this study, a formulation is suggested to give the response variability of Mindlin plate taking into account of the uncertainties in elastic modulus as well as in the thickness of plate, a geometrical parameter, and their correlation. The cubic function of thickness and the correlation between elastic modulus and thickness are incorporated into the formulation by means of the modified auto- and cross-correlation functions, which are constructed based on the general formula for n-th joint moment of random variables. To demonstrate the adequacy of the proposed formulation, a plate with various boundary conditions is taken as an example and the results are compared with those obtained by means of classical Monte Carlo simulation.

• Structural Engineering and Mechanics
• /
• v.5 no.1
• /
• pp.69-83
• /
• 1997

A new efficient hybrid/mixed thin~moderately thick plate bending element with 6-node (HM6-14) is formulated based on the Reissner-Mindlin plate bending theory. The convergence of this element is proved by error estimate theories and verified by patch test respectively. Numerical studies on such an element as HM6-14 demonstrate that it has remarkable convergence, invariability to geometric distorted mesh situations, to axial rotations, and to node positions, and no "locking" phenomenon in thin plate limit. The present element is suitable to many kinds of shape and thin~moderately thick plate bending problems. Further, in comparison with original hybrid/mixed plate bending element HP4, the present element yields an improvement of solutions. Therefore, it is an efficient element and suitable for the development of adaptive multi-field finite element method (FEM).

• Journal of the Society of Naval Architects of Korea
• /
• v.33 no.1
• /
• pp.77-89
• /
• 1996

An enormous amount of efforts has been devoted to the development of finite elements for the bending problem of thick plates, especially based on Mindlin plate theory. Here, an approximate Constant Shear Angle Theory is usually used to take a transverse shear deformation of thick plate into consideration, which cannot be effectively considered the influence of transversal warping of cross-section with an increase of thickness. It might be the best way to represent the exact cross-sectional warping of the plate. The overall objective of this study is to develop a new formulation of plate including shear deformation and transversal warping, to perform extensive parametric studies comparing its results with those from Mindlin plate formulation, and to gain further insight into the influence of shear deformation and transversal warping of thick plate.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2007.04a
• /
• pp.465-470
• /
• 2007

In order to investigate the stochastic behavior of Mindlin plate under imperfection in the material and geometrical parameters, a stochastic finite element formulation is proposed. The effects of inter-correlations between random parameters on the response variability are also observed. The contribution from the random Poisson ratio is taken into account adopting a stochastic decomposition scheme. which expands the constitutive matrix into an infinite series of sub-matrices. In order to demonstrate the adequacy of the proposed scheme, a square plate with simple and fixed support is taken as an example, and the results are compared with those given in previous research in the literature as well as with the results of Monte Carlo analysis.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.18 no.1
• /
• pp.150-159
• /
• 2014

A simplified method for the calculation of buckling and vibrational characteristics of initially stressed rectangular plate and antisymmetric angle-ply laminated plates is presented in this paper using the natural frequencies under unloading state. The equation of motion of rectangular plate with two opposite edges simply supported is investigated on the basis of Rayleigh-Ritz method and Mindlin plate theory with effect of the curvature term. The relationships of the non-dimensional natural frequencies with initial stresses the coeffcients of critical buckling and the boundaries of the dynamic principal instability region can be characterized by the non-dimensional natureal frequencies under unloading state. Numerical examples are presented to verify the simplified equations and to illustrate potential applications of the analysis.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.7 no.4
• /
• pp.83-90
• /
• 1987

The applications of reduced integration technique, addition of nonconforming modes, and their coupling to the Mindlin plate elements to improve their basic behavior are reviewed and the establishment of a series of new plate elements by combined use of these schemes are presented in this paper. The element formulation is based upon quadratic Mindlin plate concept. The results obtained by new elements converged to the exact solutions very rapidly as the mesh is refined and showed reliable solutions even for severely distorted meshes. The new elements have the requisite numbers of zero eigenvalues associated with rigid body modes to avoid the spurious zero energy modes. These elements are shown to be applicable to the wide range of plate problems, giving a high accuracy for both thick and thin plates.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2004.04a
• /
• pp.25-32
• /
• 2004

In this proposed work new finite element model for multi-delaminated plates is proposed. In the current analysis procedures of multi-delaminated plates, plate element based on Mindlin plate theory is used in order to obtain accurate results of out-of-plane displacement of thick plate. And for delaminated region, plate element based on Kirchhoff plate theory is considered. To satisfy the displacement continuity conditions, displacement vector based on Kirchhoff theory is transformed to displacement of transition element. The numerical results show that the effect of delaminations on the modal parameters of delaminated composites plates is dependent not only on the size, the location and the number of the delaminations but also on the mode number and boundary conditions. Kirchhoff based model have higher natural frequency than Mindlin based model and natural frequency of the presented model is closed to Mindlin based model.

• Journal of Ocean Engineering and Technology
• /
• v.17 no.3 s.52
• /
• pp.21-26
• /
• 2003

An iteractive Kantorovich method is presented for the vibration analysis of rectangular orthotropic thick plates. Mindlin plate characteristic functions are derived in general forms using the Kantorovich method. Initially, Timoshenko beam functions consistent with the boundary conditions of the plate were used. Through numerical calculations of natural fairs of appropriate models, it has been confirmed that the method presented is superior to the Rayleigh-Ritz analysis or the finite element analysis in both accuracy and computational efficiency.

• Structural Engineering and Mechanics
• /
• v.26 no.1
• /
• pp.43-68
• /
• 2007

Using the Mindlin-Reissner plate theory, many quadrilateral plate bending elements have been developed so far to analyze thin and moderately thick plate problems via displacement based finite element method. Here new formulation has been made to analyze thin and moderately thick plate problems using force based finite element method called Integrated Force Method (IFM). The IFM is a novel matrix formulation developed in recent years for analyzing civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper the force based new bilinear quadrilateral plate bending element (MQP4) is proposed to analyze the thin and moderately thick plate bending problems using Integrated Force Method. The Mindlin-Reissner plate theory has been used in the formulation of this element which accounts the effect of shear deformation. Standard plate bending benchmark problems are analyzed using the proposed element MQP4 via Integrated Force Method to study its performance with respect to accuracy and convergence, and results are compared with those of displacement based 4-node quadrilateral plate bending finite elements available in the literature. The results are also compared with the exact solutions. The proposed element MQP4 is free from shear locking and works satisfactorily in both thin and moderately thick plate bending situations.