• Advances in materials Research
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• v.7 no.2
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• pp.119-136
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• 2018

In this paper, static and vibration analysis for anti-symmetric cross-ply and angle- ply carbon/glass hybrid laminates rectangular composite plate are presented. In this analysis, the equations of motion for simply supported thick laminated hybrid rectangular plates are derived and obtained through the use of Hamilton's principle. The closed-form solutions of anti-symmetric cross-ply and angle- ply laminates are obtained using Navier solution. The effects of side-to-thickness ratio, aspect ratio, and lamination schemes on the fundamental frequencies loads are investigated. The study concludes that shear deformation laminate theories accurately predict the behavior of composite laminates, whereas the classical laminate theory over predicts natural frequencies. The excellent accuracy of the present analytical solution is confirmed by making some comparisons of the present results with those available in the literature. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behaviors of anti-symmetric cross-ply and angle- ply hybrid laminated composite plates.

• Steel and Composite Structures
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• v.41 no.6
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• pp.787-803
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• 2021

The size-dependent nonlinear thermomechanical vibration analysis of pre- and post-buckled tapered two-directional functionally graded (2D-FG) microbeams is presented in this study. In the context of the modified couple stress theory, the formulations are derived based on the parabolic shear deformation beam theory and von Karman nonlinear strains. Different thermomechanical material properties are assumed to be temperature-dependent and smoothly vary in both length and thickness directions using the power law and the physical neutral axis concept is employed. The nonlinear governing equations are derived using the Hamilton principle and the resulting variable coefficient equations of motion are solved using the differential quadrature method (DQM) and iterative Newton's method for clamped-clamped and simply supported boundary conditions. Comparison studies are presented to validate the derived model and solution procedure. The impacts of induced thermal moments, temperature power index, two gradient indices, nonuniform cross-section, and microstructure length scale parameter on the frequency-temperature configurations are explored for both clamped and simply supported microbeams.

• Advances in nano research
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• v.14 no.5
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• pp.475-493
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• 2023

In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.

• Structural Engineering and Mechanics
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• v.65 no.3
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• pp.213-222
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• 2018

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin's theory with shear locking free fourth order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency paramerets of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.593-605
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• 2023

This work presents a comparison between analytical and finite element analysis for bending of porous sandwich functionally graded material (FGM) plates. The plate is rectangular and simply supported under static sinusoidal loading. Material properties of FGM are assumed to vary continuously across the face sheets thickness according to a power-law function in terms of the volume fractions of the constituents while the core is homogeneous. Four types of porosity are considered. A refined higher-order shear with normal deformation theory is used. The number of unknowns in this theory is five, as against six or more in other shear and normal deformation theories. This theory assumes the nonlinear variation of transverse shear stresses and satisfies its nullity in the top and bottom surfaces of the plate without the use of a shear correction factor. The governing equations of equilibrium are derived from the virtual work principle. The Navier approach is used to solve equilibrium equations. The constitutive law of the porous FGM sandwich plate is implemented for a 3D finite element through a subroutine in FORTRAN (UMAT) in Abaqus software. Results show good agreement between the finite element model and the analytical method for some results, but the analytical method keeps giving symmetric results even with the thickness stretching effect and load applied to the top surface of the sandwich.

• Steel and Composite Structures
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• v.37 no.1
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• pp.99-115
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• 2020

This article deals with the dynamic analysis in pad concrete foundation containing Silica nanoparticles (SiO₂) subject to seismic load. In order to control the foundation smartly, a piezoelectric layer covered the foundation. The weight of the building by a column on the foundation is assumed with an external force in the middle of the structure. The foundation is located in soil medium which is modeled by spring elements. The Mori-Tanaka law is utilized for calculating the equivalent mechanical characteristics of the concrete foundation. The Kevin-Voigt model is adopted to take into account the structural damping. The concrete structure is modeled by a thick plate and the governing equations are deduced using Hamilton's principle under the assumption of higher-order shear deformation theory (HSDT). The differential quadrature method (DQM) and the Newmark method are applied to obtain the seismic response. The effects of the applied voltage to the smart layer, agglomeration and volume percent of SiO₂ nanoparticles, damping of the structure, geometrical parameters and soil medium of the structure are assessed on the dynamic response. It has been demonstrated by the numerical results that by applying a negative voltage, the dynamic deflection is reduced significantly. Moreover, silica nanoparticles reduce the dynamic deflection of the concrete foundation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.5
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• pp.1479-1485
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• 1991

본 연구에서는 고차판이론(higher order shear deformable plate theory)을 사용하여 DCB시편을 보형상이 아닌 실제의 얇은 판으로 해석하여 새로운 에너지해방률 식을 제시하고자 한다.한편, 이의 타당성을 입증하기 위하여 Gr/Ep 및 APC-2 복합 재료로 ASTM D30.02 round robin의 제안 방법에 의해 층간파괴인성치를 구하고, 또 이 강용이 제안한 Ae법에 의한 금속의 파괴인성치 결정법을 참고로 하여 미세파괴 초창기 의 층간파괴인성치를 결정하여 이론결과와 비교 검토한다.

• Advances in concrete construction
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• v.15 no.2
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• pp.137-147
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• 2023

Dynamic analysis of a shear deformable shell is investigated with accounting thickness stretching using Hamilton's principle. Through this method, the total transverse is composed into bending, shearing and stretching portions, in which the third part is responsible for deformation along the transverse direction. After computation of the strain, kinetic and external energies, the governing motion equations are derived using Hamilton's principle. A comparative study is presented before presentation of full numerical results for confirmation of the formulation and methodology. The results are presented with and without thickness stretching to show importance of the proposed theory in comparison with previous theories without thickness stretching.

• Wind and Structures
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• v.28 no.1
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• pp.49-62
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• 2019

In this paper, an analytical analysis for the study of vibratory behavior and wave propagation of functionally graded plates (FGM) is presented based on a high order shear deformation theory. The manufacture of these plates' defects can appear in the form of porosity. This latter can question and modify the global behavior of such plates. A new shape of the distribution of porosity according to the thickness of the plate was used. The field of displacement of this theory is present of indeterminate integral variables. The modulus of elasticity and the mass density of these plates are assumed to vary according to the thickness of the plate. Equations of motion are derived by the principle of minimization of energies. Analytical solutions of free vibration and wave propagation are obtained for FGM plates simply supported by integrating the analytic dispersion relation. Illustrative examples are given also to show the effects of variation of various parameters such as(porosity parameter, material graduation, thickness-length ratio, porosity distribution) on vibration and wave propagation of FGM plates.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.143-146
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• 2003

A finite element based on the efficient higher order zig-zag theory with multiple delaminations Is developed to refine the predictions of frequency and mode shapes. Displacement field through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions including delaminated interfaces as well as free hounding surface conditions of transverse shear stresses. Thus the proposed theory is not only accurate but also efficient. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Throught the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Through the natural frequency analysis and time response analysis of composite plate with multiple delaminations, the accuracy and efficiency of the present finite element are demonstrated. The present finite element is suitable in the predictions of the dynamic response of the thick composite plate with multiple delaminations.