• Smart Structures and Systems
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• v.22 no.3
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• pp.249-257
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• 2018

This study contributes to evaluate multiphase topology optimization design of plate-like elastic structures with constant thickness and Reissner-Mindlin plate theory. Stiffness and adjoint sensitivity formulations linked to Reissner-Mindlin plate potential energy of bending and shear are derived in terms of multiphase design variables. Multiphase optimization problem is solved through alternative active-phase algorithm with Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples verify efficiency and diversity of the present topology optimization method of Reissner-Mindlin elastic plates depending on multiphase and Poisson's ratio.

• Structural Engineering and Mechanics
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• v.19 no.2
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• pp.199-215
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• 2005

An assumed stress quadrilateral thin/moderately thick plate element HQP4 based on the Mindlin/Reissner plate theory is proposed. The formulation is based on Hellinger-Reissner variational principle. Static and free vibration analyses of plates are carried out. Numerical examples are presented to show that the validity and efficiency of the present element for static and free vibration analysis of plates. Satisfactory accuracy for thin and moderately thick plates is obtained and it is free from shear locking for thin plate analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1992.10a
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• pp.39-44
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• 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
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• v.5 no.1
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• pp.69-83
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• 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).

• Steel and Composite Structures
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• v.27 no.1
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• pp.27-33
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• 2018

In this study, a mixed-interpolated tensorial component 4 nodes method (MITC4) is treated as a numerical analysis model for topology optimization using multiple materials assigned within Reissner-Mindlin plates. Multi-material optimal topology and shape are produced as alternative plate retrofit designs to provide reasonable material assignments based on stress distributions. Element density distribution contours of mixing multiple material densities are linked to Solid Isotropic Material with Penalization (SIMP) as a design model. Mathematical formulation of multi-material topology optimization problem solving minimum compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples illustrate the reliability and accuracy of the present design method for multi-material topology optimization with Reissner-Mindlin plates using MITC4 elements and steel materials.

• Steel and Composite Structures
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• v.35 no.1
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• pp.129-145
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• 2020

In typical, structural topology optimization plays a significant role to both increase stiffness and save mass of structures in the resulting design. This study contributes to a new numerical approach of topologically optimal design of Mindlin-Reissner plates considering Winkler foundation and mathematical formulations of multi-directional variable thickness of the plate by using multi-materials. While achieving optimal multi-material topologies of the plate with multi-directional variable thickness, the weight information of structures in terms of effective utilization of the material at the appropriate thickness location may be provided for engineers and designers of structures. Besides, numerical techniques of the well-established mixed interpolation of tensorial components 4 element (MITC4) is utilized to overcome a well-known shear locking problem occurring to thin plate models. The well-founded mathematical formulation of topology optimization problem with variable thickness Mindlin-Reissner plate structures by using multiple materials is derived in detail as one of main achievements of this article. Numerical examples verify that variable thickness Mindlin-Reissner plates on Winkler foundation have a significant effect on topologically optimal multi-material design results.

• Structural Engineering and Mechanics
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• v.48 no.1
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• pp.77-91
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• 2013

The paper presents the formulation of 3-nodal line semi-analytical Mindlin-Reissner finite strip in the buckling analysis of thin-walled members, which are subjected to arbitrary loads. The finite strip is simply supported in two opposite edges. The general loading and in-plane rotation techniques are used to develop this finite strip. The linear stiffness matrix and the geometric stiffness matrix of the finite strip are given in explicit forms. To validate the proposed model and study its performance, numerical examples of some thin-walled sections have been performed and the results obtained have been compared with finite element models and the published ones.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.151-160
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• 1993

This paper is concerned with formulations of the hierarchical $C^{\circ}$-plate element on the basis of Reissner-Mindlin plate theory. On reason for the development of the aforementioned element based on Integrals of Legendre shape functions 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 are proposed to verify the superior convergence and algorithmic efficiency with the help of the simply supported L-shaped plate problems.

• Structural Engineering and Mechanics
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• v.41 no.2
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• pp.205-229
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• 2012

This paper presents a new nine-node Lagrangian quadrilateral plate bending element (MQP9) using the Integrated Force Method (IFM) for the analysis of thin and moderately thick plate bending problems. Three degrees of freedom: transverse displacement w and two rotations ${\theta}_x$ and ${\theta}_y$ are considered at each node of the element. The Mindlin-Reissner theory has been employed in the formulation which accounts the effect of shear deformation. Many standard plate bending benchmark problems have been analyzed using the new element MQP9 for various grid sizes via Integrated Force Method to estimate defections and bending moments. These results of the new element MQP9 are compared with those of similar displacement-based plate bending elements available in the literature. The results are also compared with exact solutions. It is observed that the presented new element MQP9 is free from shear locking and produced, in general, excellent results in all plate bending benchmark problems considered.

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