This research investigates buckling behavior of a clamped sandwich panel resting on elastic Winkler foundation using differential quadrature method. The sandwich panel has a symmetric structure with an isotropic core encapsulated by two symmetric orthotropic and isotropic layers. The governing differential equations are derived based on the first order shear deformation theory and solved numerically using differential quadrature method. The boundary conditions are assumed to be clamped. The numerical results are compared with those finite element method. Good accuracy is observed between two methods. The effect of geometric parameters such as panel aspect ratio, ratio of the core to the cover layers thicknesses, as well as the ratio of the panel length to its thickness is investigated buckling load. The results confirm the Increasing aspect ratio reduces critical loads and also increasing the thickness of the core causing increases buckling load.

 In this study, the free vibration of a clamped sandwich plate using the generalized differential quadrature method is investigated. This plate is located on a single-parameter elastic foundation known as Winkler foundation. To obtain the governing equations of the plate, the first order shear deformation theory as well as Hamilton's principle are used. By applying the generalized differential quadrature method to the equations, the system of equations are achieved. Mode shapes and natural frequencies of the plate are then calculatedby solving an eigenvalue problem. Finally, the obtained results are compared with other existing methods such as Galerkin and finite element method. Moreover the effect of changing some geometrical parameters is investigated on the natural frequencyof the plate. This comparison showed the high accuracy of the proposed method for the solving free vibrations of clamped sandwich plate on the elastic foundation. Based on the results of this study, adding an elastic foundation to the sandwich plate, increasesthe natural frequency.Also, by increasing the thickness of sandwich plate core led the increase in natural frequencies.

In this work, shear stress distribution in an adhesive joint in presence of a yielded matrix has been studied. The bonded layers are assumed to form a single lap joints. To extract the analytical solution, it is assumed that the adhesive layer behaves as elastic-perfectly plastic while the adherends have a linear elastic behavior. The results based on analytical solution are compared with finite element findings. Additionally, to study the effect of geometric and physical parameters on final results, a relationship between the applied load and the yielded region in the adhesive is also extracted. Among these parameters one may point to the length of the adhesive joint, thickness of the adhesive and adherends layers and Young's modulus of each adherends layer. According to the results, any increase in the adherends and adhesive thicknesses causes a reduction in the length of the yielded region. Moreover, holding the bending stiffness of the bottom layer as a constant, any increase in elastic modulus and thickness of the top adherend layer reduces the maximum shear stress developed in adhesive layer (the opposite effect was also observed).

 : In this thesis, , the distribution of stresses in composite’s single-lap joints are optimized by changing layers. The adhesive layer assumed to be a linear alestic layer. To determine an appropriate mathematical model for calculating the stress values, two-dimensional first-order shear deformation theory in the analysis of adherends. Stresses in adhesive layer are constant in thickness direction. All of the cracks and defects have been connivanced. By forming equilibrium equations of cross sections, some equation between forces and momentoms of adherend and adhesive’s stresses have been formed. Adhesive layer’s strains defined by adherend’s movement and finally by combining of all equation, a defferential equation formed. By solving this defferential equation and some boundary conditions, stress distribution’s functions will be determined. After deteminding the appropriate the distribution of shear stress and peel stress , results are compared with datas that obtained by finite element model simulated in ANSYS software. An excellent agreement is observed between analytical and FE method’s results. Optimization process have been done by using the single objective bees algorithm, and multi-objective NSBA-II algorithm. At last layer arrangement of each laminate has been optimized and results of any circumstances have been shown in tables. Turns out that decrease in adherend’s angles may decrease shear stress in adhesive layer and an increase in adherend’s angles may increase shear stress in adhesive layer. For peeling stress turn out that by arranging high angle layers in inner area and low angle layers in outer area may minimize peeling stress.

This research has study the effect of sandwich shape core like honeycomb, triangle and square on stress intensity factor at interface crack tip by finite element method. This crack is edge crack shape and located in cohesive and between core and face. Also cells core has been change in to continuum core that it’s treatment like to cells core in elastic region. The crack has been study by fracture mechanics by Assumption that crack located in the middle of cohesive layer, delaminated region of face and core has no defect and has mechanical properties as another regions and defected zone is small according to the another region. According to result of changing cells core to continuum one by finite element method, theoretical relation for cell cores had make by isotropic materials are true and number of cells effect on mechanical properties of continuum core and by raising number of them has been change and converge to amount of theoretical relations. These theoretical relations had upgrade to composite materials and had correct by finite element method. According to result of studding interface crack, stress intensity factor at crack tip raise by raising cell core’s thickness and stress intensity factor at interface crack tip of honeycomb core shape in the both condition (mode I, compound of mode I and mode II) is smaller than two other shapes.

In this thesis, the inter-laminate adhesive peel and shear stress in balanced bonded stiffened and single-strap butt joints are thoeritically and numerically presented. The first order and classical laminate plate theory based on adhesive interface constitutive model are employed for this deduction. This approach takes into account the elastic behaviuor of both adhesive and adherents layer, while the adhesive layer is assumed to be isotropic, the adherents are considered as generally orthotropic material subjected to in-plane and out of–plane load conditions. Although, the length variying of adhesive layer in a stiffened joints and the effect of applying stiffeners and its geometrical properties on single-strap joint, in the distribution of the inter-laminate stresses have been investigated. The results are validated by FEM solution. An excellent agreement is observed between analytical and FE methods. In such a case, as expected, since the bending stiffeness of the joint will gradually rise up, the deflection in the deflection in overlap area reaches the minimum value, consequently, the results obtained, portray decreasing trends in the value of the peak peel and shear stresses in contrast to the case where no stiffeners are applied.

In this thesis, the interfacial stresses in tubular single lap adhesively bonded joints in the presence of defect (void and debond) subjected to torsional and axial loads is studied. It is assumed that the shear stress varies along the adhesive thickness and the mechanical and geometrical properties of the tube may differ with each other. A quadratic displacement field along the adhesive thickness is assumed. The solution is based on the elasticity theory that include the complete equilibrium equations, stress-strain and strain-displacement. Also the change in elasticity module of both adhesive and tubes are taken into account. The results are validated by FE method. An excellent agreement is observed between analytical and FE method. By changing some of the adhesive and adherents’ characteristics, the results show that, as the adhesive and the adherent Young’s modulus are increased, the maximum value of the stresses will increase and falls down, respectively. The results implies that the presence of imperfection such as void and debond in the overlap region, will cause in increasing the value of shear stress in the region close to the imperfection. This increase depends on the length and especially the locations where the defects occurred.

In this thesis, the distribution of the inter-laminate peeling stresses and shear stresses in a single-lap joint is studied. The adhesive layer under study is assumed to be isotropic while each of the adherents are general orthotropic in nature and are subjected under bending moments. The properties and thickness of each adherents may differ with the other but the lay-up is assumed to be symmetric. A linear elasticity is assumed for both adherents and in the adhesive layer .The solution is based on a two-dimensional and first order laminate plate theory and the stress distribution is assumed to be constant along the adhesive thickness. Also the change in elasticity modulus, thickness and the length of the adhesive layer, the adherent’s thickness, the angle and the fiber’s layout have been taken into account. By changing some of the adhesive and adherents’ characteristics, the results show that, the adhesive and the adherent thicknesses are increased, as well as the adherents Young’s modulus, the maximum value of the stresses will be decreased but by increasing the adhesive young’s modulus, the maximum value of the stresses will rise up. The results are validated by FEM solution. An excellent agreement is observed between analytical and FE methods. It is observed that the results developed within the adhesive layer is function of mechanical and physical parameters as Young’s modulus, Poisson’s ratio and thickness and the fiber layout in matrix.

 In this thesis, stress distributioin in components of a single-lap joint under axial and bending loads composed of plain woven composite adherends is studied using finite element method via ANSYS Workbench. In this analysis at first proper tensile forces and bending moments are obtained. Then the effect of parameters such as looseness factor (the space between yarns), adhesive thickness, adhesive length, modulus of elasticity and Poisson’s coefficient on the stresses applied to the adhesive and the adherends components composed of matrix and yarns is studied. The results show that the main part of the applied loads is tolerated by sets of yarns, especially warp yarns which are in the direction of applied loads. In addition, stress in the used yarns is much less than their tensile strength; so the fracture cannot happen in the yarns. Peeling stress is the main factor of fracture in the adhesive joints which should be minimized. Results indicate that increase in parameters such as looseness factor, adhesive thickness and adhesive length and decrease in parameters such as modulus of elasticity and adhesive Poisson’s coefficient will lead to decrease in stress in joint components. In other words, the joint strength will increase.