• Structural Engineering and Mechanics
• /
• 제40권4호
• /
• pp.501-515
• /
• 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
• /
• 제7권5호
• /
• pp.473-484
• /
• 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.

• Advances in nano research
• /
• 제12권5호
• /
• pp.441-455
• /
• 2022

This study explores the linear and nonlinear solutions of sigmoid functionally graded material (S-FGM) nanoplate with porous effects. A size-dependent numerical solution is established using the strain gradient theory and isogeometric finite element formulation. The nonlinear nonlocal strain gradient is developed based on the Reissner-Mindlin plate theory and the Von-Karman strain assumption. The sigmoid function is utilized to modify the classical functionally graded material to ensure the constituent volume distribution. Two different patterns of porosity distribution are investigated, viz. pattern A and pattern B, in which the porosities are symmetric and asymmetric varied across the plate's thickness, respectively. The nonlinear finite element governing equations are established for bending analysis of S-FGM nanoplates, and the Newton-Raphson iteration technique is derived from the nonlinear responses. The isogeometric finite element method is the most suitable numerical method because it can satisfy a higher-order derivative requirement of the nonlocal strain gradient theory. Several numerical results are presented to investigate the influences of porosity distributions, power indexes, aspect ratios, nonlocal and strain gradient parameters on the porous S-FGM nanoplate's linear and nonlinear bending responses.

• 대한기계학회논문집
• /
• 제12권3호
• /
• pp.481-488
• /
• 1988

본 연구에서는 판이론으로서는 해석할수 없는 집중충격하중의 작용점을 포함 한 유한판(정방형판)의 충격응력을 이론적으로 해석하는 방법을 제안하고저 하며 포성 재료로서 손쉽게 구할수 있고 파괴에 큰 에너지가 소요되지 않은 유리판을 대상으로 하여 3차원 동탄성이론을 이용하여 강구의 고속충돌에 의해서 유리판에 발생하는 충격 응력을 해석하였다. 또한 3차원 동탄성이론에서는 Laplace역변환이 곤난하므로, 고 속 Fourier변환의 알고리즘을 이용하였으며, 충격하중의 크기는 실측이 곤난하여 Lag- range의 고유판이론과 Hertz의 접촉이론으로부터 결정하였으며 단순지지된 정방형유리 판에 고속충격을 가하여 계측된 변형율변동과 본이론해석 결과와를 비교하여 응력해석 방법의 적용성을 명확히 하였다.

• Structural Engineering and Mechanics
• /
• 제44권4호
• /
• pp.431-448
• /
• 2012

In this paper, the first-order shear deformation theory (FSDT) (Mindlin) for continuum incorporating surface energy is exploited to study the static behavior of ultra-thin functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. By incorporating the surface energies into the principle of minimum potential energy, a series of continuum governing differential equations which include intrinsic length scales are derived. The modifications over the classical continuum stiffness are also obtained. To illustrate the application of the theory, simply supported micro/nano scaled rectangular films subjected to a transverse mechanical load are investigated. Numerical examples are presented to present the effects of surface energies on the behavior of functionally graded (FG) film, whose effective elastic moduli of its bulk material are represented by the simple power law. The proposed model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. Also, the transverse shear strain effect is studied by a comparison between the FG plate behavior based on Kirchhoff and Mindlin assumptions. In our analysis the residual surface tension under unstrained conditions and the surface Lame constants are expected to be the same for the upper and lower surfaces of the FG plate. The proposed model is verified by previous work.

• Steel and Composite Structures
• /
• 제24권2호
• /
• pp.151-176
• /
• 2017

This paper deals with general equations of motion for free vibration analysis response of thick three-layer doubly curved sandwich panels (DCSP) under simply supported boundary conditions (BCs) using higher order shear deformation theory. In this model, the face sheets are orthotropic laminated composite that follow the first order shear deformation theory (FSDT) based on Rissners-Mindlin (RM) kinematics field. The core is made of orthotropic material and its in-plane transverse displacements are modeled using the third order of the Taylor's series extension. It provides the potentiality for considering both compressible and incompressible cores. To find these equations and boundary conditions, Hamilton's principle is used. Also, the effect of trapezoidal shape factor for cross-section of curved panel element ($1{\pm}z/R$) is considered. The natural frequency parameters of DCSP are obtained using Galerkin Method. Convergence studies are performed with the appropriate formulas in general form for three-layer sandwich plate, cylindrical and spherical shells (both deep and shallow). The influences of core stiffness, ratio of core to face sheets thickness and radii of curvatures are investigated. Finally, for the first time, an optimum range for the core to face sheet stiffness ratio by considering the existence of in-plane stress which significantly affects the natural frequencies of DCSP are presented.

• Advances in nano research
• /
• 제6권4호
• /
• pp.299-321
• /
• 2018

A layerwise shear deformation theory is applied in this paper for buckling analysis of piezoelectric truncated conical shell. The core is a multiphase nanocomposite reinforced by carbon nanotubes (CNTs) and carbon fibers. The top and bottom face sheets are piezoelectric subjected to 3D electric field and external voltage. The Halpin-Tsai model is used for obtaining the effective moisture and temperature dependent material properties of the core. The proposed layerwise theory is based on Mindlin's first-order shear deformation theory in each layer and results for a laminated truncated conical shell with three layers considering the continuity boundary condition. Applying energy method, the coupled motion equations are derived and analyzed using differential quadrature method (DQM) for different boundary conditions. The influences of some parameters such as boundary conditions, CNTs weight percent, cone semi vertex angle, geometrical parameters, moisture and temperature changes and external voltage are investigated on the buckling load of the smart structure. The results show that enhancing the CNTs weight percent, the buckling load increases. Furthermore, increasing the moisture and temperature changes decreases the buckling load.

• 한국철도학회:학술대회논문집
• /
• 한국철도학회 2011년도 정기총회 및 추계학술대회 논문집
• /
• pp.2632-2634
• /
• 2011

In the Structural Health Monitoring field, the piezoelectric elements are bonded the surface of the structures for generating the guided wave. For this reason, the structures become two-layer beam. It is very important to know precisely the dynamic characteristic of structures and also predict precisely the wave propagation in structures. Because wave propagation is very useful to analysis the dynamic characteristic of structures. In this paper, the governing equations of motion are derived from Hamilton's principle by applying the Timoshenko beam theory and Mindlin-Herrmann rod theory at the first. and then the wave propagations in a composite beams with a surface-bonded piezoelectric are examined.

• International Journal of Naval Architecture and Ocean Engineering
• /
• 제6권4호
• /
• pp.763-774
• /
• 2014

A simple and efficient vibration analysis procedure for stiffened panels with openings and arbitrary boundary conditions based on the assumed mode method is presented. Natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion, where Mindlin theory is applied for plate and Timoshenko beam theory for stiffeners. The effect of stiffeners on vibration response is taken into account by adding their strain and kinetic energies to the corresponding plate energies whereas the strain and kinetic energies of openings are subtracted from the plate energies. Different stiffened panels with various opening shapes and dispositions for several combinations of boundary conditions are analyzed and the results show good agreement with those obtained by the finite element analysis. Hence, the proposed procedure is especially appropriate for use in the preliminary design stage of stiffened panels with openings.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1997년도 가을 학술발표회 논문집
• /
• pp.73-79
• /
• 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.