---

In this paper, a novel four-variable refined theory of plate, called RPT, has been proposed for free vibration of composite laminated plates, using a hyperbolic sine function, for calculating out-of-plane shear strains. It is one of the properties of this theory that the boundary condition of zero shear stress is satisfied over upper layer and under lower layer of plate, with no reference to Timoshenko shape factor. In contrast to other higher-order shear deformation theories, in RPT theory, equations of motion are coupled dynamically only in inertial terms, while elastic energy terms are not coupled for the variables used. From this viewpoint, RPT theory is similar to classical plate theory (CLPT). Some of the objectives of this paper are the investigation of effect of influential parameters on fundamental frequency, such as modulus ratio, angle of plies, and plate length-to-thickness ratio. The results of this proposed version of RPT are compared and validated with those of first-order shear deformation theory (FSDT), higher-order shear deformation theory (HSDT), and the original version of RPT.

---

In this paper, interlaminar stresses resulting from static behavior of laminated plates, which were made from composite materials, were evaluated. To this end, out-of-plane stresses and displacements were considered as a primary variable. In addition, for the problem analysis, the boundary value problem method was expanded in order to form a first-order linear differential equations system which depended on the laminate thickness. This method could consider normal and transverse stresses and investigates a three-dimensional stress field near the free edge of the layers. In the proposed model, a laminated plate was placed on a simply supported boundary condition and under transverse loading. It was also assumed that the interlaminar transverse stresses, and displacements were continuous in layers' interfaces. The governing differential equations system was solved using Navier's approach and shooting method and, finally, the obtained results were compared with the results of other references. The results indicated good accuracy and high speed of the method used in analyzing stress field.

---

In this study, nonlinear bending analysis of ring-stiffened annular laminated composite plates is studied. A discretely stiffened plate theory for elastic large deflection analysis of uniformly distributed loaded is introduced. The governing equations are derived based on a first-order shear deformation plate theory (FSDT) and large deflection von Karman equations. The numerical results are obtained using the dynamic relaxation (DR) method combined with the central finite difference discretization technique. For this purpose, a FORTRAN computer program is developed to generate the numerical results. In order to verify the accuracy of the present method the results are compared with those available in the literatures and ABAQUS finite element package as well. The computer code can handle symmetric, unsymmetrical and general theta-ply schemes. The effects of the plate thicknesses, different ratio of outer to inner radius, depth of stiffener, boundary condition and laminates lay-up are studied in detail.

---

Magnetorheological (MR) materials indicate variations in their rheological properties when subjected to different magnetic fields. This study presents vibration analysis of laminated composite plates using MR fluid lumps. A structural dynamic modeling approach is presented to investigate the vibration characteristics of MR adaptive structures for different magnetic fields. The effects of laminate configurations and locations of MR fluid lamps on the controlled response are investigated. Vibration responses of the laminated plate have been simulated to demonstrate the accuracy and efficiency of the present approach. The results of this work may improve the dynamic performance of composite structures which are subjected to undesirable vibration during operation such as helicopters blades

---

In this paper, post-buckling behavior of laminated plates is investigated using mesh-free method. One of the most common powerful numerical methods in recent decades is mesh-free collocation method. Due to wildly oscillating solutions at the endpoints and occurrence of Runge phenomenon in the case of uniform distribution of points, the domain of the problem is discretized with Legendre-gauss-lobatto nodes. In this paper, the classical laminated plate theory is used and different out-of-plane boundary conditions with anti-symmetric cross-ply and angle-ply laminates are investigated. Equations system is introduced by discretizing von-Karman’s compatibility equations and boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Because of large deformations and nonlinear terms in the strain-displacement relations, the nonlinear system of equations is solved by using Newton-Raphson technique. Since number of equations is always more than the number of unknown parameters, the least square technique is used to solve the system of equations. Some results are obtained and compared with those available in the literature.