• Structural Engineering and Mechanics
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• v.40 no.4
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• pp.501-515
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• 2011

Sandwich elements have high flexural rigidity and high strength per density. They also have excellent anti-vibration and anti-noise characteristics. Therefore, they are used for structures of airplanes and high speed ships that must be light, as well as strong. In this paper, the Reissner-Mindlin's plate theory is studied from a Hamilton's principle point of view. This theory is modified to include the influence of shear deformation and rotary inertia, and the equation of motion is derived using energy relationships. The theory is applied to a rectangular sandwich model which has isotropic, asymmetrical faces and an isotropic core. Investigations are conducted for five different plate thicknesses. These plates are identical to the sandwich plates currently used in various structural elements of surface effect ships (SES). The boundary conditions are set to simple supports and fixed supports. The elastic and shear moduli are obtained from the four-point bending tests on the sandwich beams.

• Structural Engineering and Mechanics
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• v.7 no.5
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• pp.473-484
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• 1999

In the present study, the thermal buckling analysis of thick anisotropic laminated composite plates is carried out using the finite strip method based on the higher-order shear deformation theory. This theory accounts for the parabolic distribution of the transverse shear strains through the thickness of the plate and for zero transverse shear stresses on the plate surfaces. Therefore, this theory yields improved results over the Mindlin plate theory and eliminates the need for shear correction factors in calculating the transverse shear stiffness. The critical temperatures of simply supported rectangular cross-ply and angle-ply composite laminates are calculated. The effects of several parameters, such as the aspect ratio, the length-to-thickness ratio, the number of plies, fibre orientation and stacking sequence, are investigated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.71-81
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• 2008

This paper proposes a spectral element which can represent dynamic responses in high frequency domain such as Lamb waves on a thin plate. A two layer beam model under 2-D plane strain condition is introduced to simulate high-frequency dynamic responses induced by piezoelectric layer (PZT layer) bonded on a base plate. In the two layer beam model, a PZT layer is assumed to be rigidly bonded on a base beam. Mindlin-Herrmann and Timoshenko beam theories are employed to represent the first symmetric and anti-symmetric Lamb wave modes on a base plate, respectively. The Bernoulli beam theory and 1-D linear piezoelectricity are used to model the electro-mechanical behavior of a PZT layer. The equations of motions of a two layer beam model are derived through Hamilton's principle. The necessary boundary conditions associated with electro mechanical properties of a PZT layer are formulated in the context of dual functions of a PZT layer as an actuator and a sensor. General spectral shape functions of response field and the associated boundary conditions are formulated through equations of motions converted into frequency domain. A detailed spectrum element formulation for composing the dynamic stiffness matrix of a two layer beam model is presented as well. The validity of the proposed spectral element is demonstrated through comparison results with the conventional 2-D FEM and the previously developed spectral elements.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.11
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• pp.1157-1169
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• 2008

This paper presents spectral element formulation which approximates Lamb wave propagation by PZT transducers bonded on a thin plate. A two layer beam model under 2-D plane strain condition is introduced to simulate high-frequency dynamic responses induced by a piezoelectric (PZT) layer rigidly bonded on a base plate. Mindlin-Herrmann and Timoshenko beam theories are employed to represent the first symmetric and anti-symmetric Lamb wave modes on a base plate, respectively. The Euler-Bernoulli beam theory and 1-D linear piezoelectricity are used to model the electro-mechanical behavior of a PZT layer. The equations of motions of a two layer beam model are derived through Hamilton's principle. The necessary boundary conditions associated with the electro-mechanical properties of a PZT layer are formulated in the context of dual functions of a PZT layer as an actuator and a sensor. General spectral shape functions of response field and the associated boundary conditions are obtained through equations of motions converted into frequency domain. Detailed spectrum element formulation for composing the dynamic stiffness matrix of a two layer beam model is presented as well. The validity of the proposed spectral element is demonstrated through numerical examples.

• Structural Engineering and Mechanics
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• v.50 no.2
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• pp.181-199
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• 2014

Locking phenomenon is a mesh problem and can be staved off with mesh refinement. If the studier is not preferred going to the solution with increasing mesh size or the computer memory can stack over flow than using higher order plate finite element or using integration techniques is a solution for this problem. The purpose of this paper is to show the shear locking phenomenon can be avoided by increase low order finite element mesh size of the plates and to study shear locking-free analysis of thick plates using Mindlin's theory by using higher order displacement shape function and to determine the effects of various parameters such as the thickness/span ratio, mesh size on the linear responses of thick plates subjected to uniformly distributed loads. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 4-, 8- and 17-noded quadrilateral finite elements are used. It is concluded that 17-noded finite element converges to exact results much faster than 8-noded finite element, and that it is better to use 17-noded finite element for shear-locking free analysis of plates.

• Steel and Composite Structures
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• v.48 no.5
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• pp.583-597
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• 2023

This paper introduces a novel approach to multi-material topology optimization (MTO) targeting in-plane bi-directional functionally graded (IBFG) non-uniform thickness Reissner-Mindlin plates, employing an alternative active phase approach. The mathematical formulation integrates a first shear deformation theory (FSDT) to address compliance minimization as the objective function. Through an alternating active-phase algorithm in conjunction with the block Gauss-Seidel method, the study transforms a multi-phase topology optimization challenge with multi-volume fraction constraints into multiple binary phase sub-problems, each with a single volume fraction constraint. The investigation focuses on IBFG materials that incorporate adequate local bulk and shear moduli to enhance the precision of material interactions. Furthermore, the well-established mixed interpolation of tensorial components 4-node elements (MITC4) is harnessed to tackle shear-locking issues inherent in thin plate models. The study meticulously presents detailed mathematical formulations for IBFG plates in the MTO framework, underscored by numerous numerical examples demonstrating the method's efficiency and reliability.

• Advances in aircraft and spacecraft science
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• v.3 no.2
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• pp.113-148
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• 2016

In a whole variety of higher order plate theories existing in the literature no consideration is given to the transverse normal strain / deformation effects on flexural response when these higher order theories are applied to shear flexible composite plates in view of minimizing the number of unknown variables. The objective of this study is to carry out cylindrical bending of simply supported laminated composite and sandwich plates using sinusoidal shear and normal deformation plate theory. The most important feature of the present theory is that it includes the effects of transverse normal strain/deformation. The displacement field of the presented theory is built upon classical plate theory and uses sine and cosine functions in terms of thickness coordinate to include the effects of shear deformation and transverse normal strain. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the shear stress free conditions at the top and bottom surfaces of the plate without using the problem dependent shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of minimum potential energy. The accuracy of the proposed theory is examined for several configurations of laminates under various static loadings. Some problems are presented for the first time in this paper which can become the base for future research. For the comparison purpose, the numerical results are also generated by using higher order shear deformation theory of Reddy, first-order shear deformation plate theory of Mindlin and classical plate theory. The numerical results show that the present theory provides displacements and stresses very accurately as compared to those obtained by using other theories.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.73-79
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• 1997

It is one of classical problems in the elastic theory to analyze contact stresses between elastic bodies. Concrete pavements under traffic wheel loads can be considered as one of these typical Problems. In the paper, Mindlin plate theory is used to consider the transverse shear effect, 8-node isoparametric plate bending element is adopted in this study, and an elastic plate resting on tensionless elastic half-space is analyzed by finite element method. The Boussineq's solution of elastic half-space is used to evaluate the flexibility of foundation. To obtain the boundary of contact area, the flexibility matrix of foundation is modified after each cycle of analysis iteratively. A Numerical example is presented by using these method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.3
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• pp.481-488
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• 1988

In the analysis of impulsive response of plate, Lagrange's theory, Reissner's theory and Mindlin's theory are generally used. But, in applying these theories the impulsive stresses directly underneath the concentrated impact point cannot be analyzed because the solution fails to converge. In this paper, therefore, an attempt for a supported square plate is made by using three-dimensional dynamic theory of elasticity on the supposition that the uniform distributed load acts on the central part of it. In order to clarify the validity of theoretical analysis, the strain variations are measured experimentally for a square glass plate. Finally it is shown that these theoretical results are in close agreement with the experimental results.

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