In this paper, the low-velocity impact response of composite plates in the presence of pre-loads is investigated using three new models for contact force estimation. The boundary conditions are considered as simply supported and the behavior of the material is linear elastic. The equations are based on both classical and first order shear deformation theory and the Fourier series method is used to solve the governing equations. The mass of the impactor is considered to be large mass and therefore the impact response is categorized as quasi-static. In the first impact model, the contact force history is first considered as a half-sine and then the maximum contact force and contact duration are calculated. In the second model, an improved two degree of freedom (ITDOF) spring-mass system is expressed by calculating the effective contact stiffness using a fast-iterative scheme. In the third model, which is expressed for the first time in this paper, the plate is considered as a series of masses and springs constructing a multi degree of freedom (MDOF) spring-mass system and the average forces applied to springs is introduced as the contact force. Validation of these models is done by comparing the results with the analytical, numerical and experimental results and shows good agreement. Results show that the new MDOF spring-mass system is more accurate for calculating the contact force rather than the ITDOF spring-mass system.
In this research the free vibration analysis of simply supported grid stiffened doubly curved shells by using a refined higher order theory is presented. The advantage of the present theory in comparison with other higher order theories is investigation of the effects of trapezoidal shape factor in the stress resultants in order to obtain more accurate frequency results. The governing equations of motion and boundary conditions are obtained using Hamilton’s principle and solved by using the Galerkin method. In the case of grid stiffened shells, a distribution function is introduced for describing the physical discontinuity between the ribs and the bays. The results are validated by making comparison to those existed in the literature or those obtained using the present numerical simulation in ABAQUS/Standard solver. In most cases, validations illustrated excellent agreement between the results . Finally, the effects of geometrical properties, material property and layup on the frequency responses of the shell are discussed.
In this study, the transient dynamic analysis of grid-stiffened composite conical shells is discussed. The transient dynamic response of the composite conical shell with simply supported boundary conditions under the lateral impact load, which is applied extensively and uniformly on a certain surface, is obtained using the convolution integral and based on the method of addition of modes. The validation of the obtained results has been done with the help of references and ABAQUS finite element software. The effects of various parameters such as fiber angle, geometric ratios, type, etc. have been investigated in forced vibrations. Finally, the effect of reinforcing the conical shell with the help of grid-stiffened structures has been studied.The effects of various parameters such as fiber angle, geometric ratios, type, etc. have been investigated in forced vibrations. Finally, the effect of reinforcing the conical shell with the help of grid-stiffened structures has been studied.grid-stiffened structures has been studied.
In this paper, free vibration analysis of damaged functionally graded beams based on the first-order shear deformation theory (FSDT) is carried out. In this regard, a new model of springs is introduced to model the damaged elements of the beam. The proposed model is achieved from stress resultants. The springs equations for homogeneous and functionally graded (FG) beams are presented; furthermore, equations for equivalent springs are also provided which can be used for both homogeneous and FG beams. The proposed method can be applied for the analysis of structures with fewer computation costs and high accuracy. To show the accuracy of the proposed model, the natural frequencies of the beams with real elements and the ones which are modeled by the proposed springs are compared considering various support conditions. Good agreement has been observed. Thereafter, the model is used to detect the damaged elements. The result shows that the model can properly detect the damage location.
The article presents the study of the stress state of a two-layer composite with a cylindrical cavity located parallel to the surfaces of the layers. Displacements are set on the cavity and the upper and lower boundaries of the upper and lower layers, respectively. The three-dimensional elasticity solution has been obtained by the analytical-numerical generalized Fourier method with respect to the system of Lame equations in local cylindrical coordinates associated with cavity and Cartesian coordinates associated with boundaries of the layers. The infinite systems of linear algebraic equations resulting from satisfying the boundary conditions are solved by the reduction method. As a result, displacements and stresses have been obtained at various points of the elastic body. We have compared the stress-strain state of a two-layer structure with a cylindrical cavity located in either of the layers. The analysis included various geometrical parameters and boundary functions; the results obtained were compared with a single-layer holed structure.
