Search Results (4)

This study aimed to provide a static solution to the boundary value problem presented by symmetric (0°/90°/0°) and antisymmetric (0°/90°) cross-ply composite, moderately thick shallow shells and plates (a special case of the shells) subjected to mixed-type unsolved boundary conditions. The boundary-discontinuous double Fourier series (BDM) method, in which displacements are expressed in trigonometric functions, is employed in a well-established framework. The analytical solution obtained using the BDM is compared with the successful integration of the generalized differential quadrature (GDQ) method for the static analysis of composite shells with a roller skate-type boundary condition prescribed on two opposite edges, while the remaining two edges are subjected to simply supported constraints. Comprehensive results are presented in order to show the effects of curvature on the deflections and stresses of moderately thick shallow shells made up of symmetric and antisymmetric cross-ply laminated composite materials. The validity of the proposed model is authenticated through the available HSDT-based literature review, and the convergence characteristics are demonstrated. The changing trends of displacements and stresses are explained in detail by investigating the effect of various parameters such as lamination, material properties, the effect of curvature, etc. Based on the results obtained using the proposed static solution, analytical BDM results were found to be in very close agreement with the numerical GDQ method, especially for symmetric lamination. However, the results obtained using the BDM and GDQ methods for antisymmetric lamination show differences, possibly due to the presence of a discontinuity in the derivatives originating from the bending–stretching matrix in antisymmetric lamination. Important numerical results presented include the sensitivity of the predicted response quantities of interest to material properties, lamination, and thickness effects, as well as their interactions. The results presented here may also serve as benchmark comparison points with numerical solutions such as finite elements, boundary elements, etc. Full article

In this paper, a new four-variable refined shell theory is developed for free vibration analysis of multi-layered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) doubly curved shallow shell panels. The theory has only four unknowns and satisfies zero stress conditions at the free surfaces without correction factor. Five different types of carbon nanotube (CNTs) distribution through the thickness of each FG-CNT layer are considered. Governing equations of simply supported doubly curved FG-CNTRC panels are derived from Hamilton’s principle. The resultant eigenvalue system is solved to obtain the frequencies and mode shapes of the anti-symmetric cross-ply laminated panels by using the Navier solution. The numerical results in the comparison examples have proved the accuracy and efficiency of the developed model. Detailed parametric studies have been carried out to reveal the influences of CNTs volume fraction, CNTs distribution, CNTs orientation, dimension ratios and curvature on the free vibration responses of the doubly curved laminated FG-CNTRC panels. Full article

In this paper, a semi-analytical method is adopted to analyze the free vibration characteristics of composite laminated shallow shells under general boundary conditions. Combining two kinds of shell theory, that is, first-order shear deformation shell theory (FSDT) and classical shell theory (CST), to describe the dynamic relationship between the displacement resultants and force vectors, the theoretical formulations are established. According to the presented work, the displacement and transverse rotational variables are transformed into wave function forms to satisfy the theoretical formulation. Related to diverse boundary conditions, the total matrix of the composite shallow shell can be established. Searching the determinant of the total matrix using the dichotomy method, the natural frequency of composite laminated shallow shells is obtained. Through several classical numerical examples, it is proven that the results calculated by the presented method are more accurate and reliable. Furthermore, to discuss the effect of geometric parameters and material constants on the natural frequencies of composite laminated shallow shells, some numerical examples are calculated to analyze. Also, the influence of boundary elastic restrained stiffness is discussed. Full article

The pressure hull is the primary element of submarine, which withstands diving pressure and provides essential capacity for electronic systems and buoyancy. This study presents a numerical analysis and design optimization of sandwich composite deep submarine pressure hull using finite element modeling technique. This study aims to minimize buoyancy factor and maximize deck area and buckling strength factors. The collapse depth is taken as a base in the pressure hull design. The pressure hull has been analyzed using two composite materials, T700/Epoxy and B(4)5505/Epoxy, to form the upper and lower faces of the sandwich composite deep submarine pressure hull. The laminated control surface is optimized for the first ply failure index (FI) considering both Tsai–Wu and maximum stress failure criteria. The results obtained emphasize an important fact that the presence of core layer in sandwich composite pressure hull is not always more efficient. The use of sandwich in the design of composite deep submarine pressure hull at extreme depths is not a safe option. Additionally, the core thickness plays a minor role in the design of composite deep submarine pressure hull. The outcome of an optimization at extreme depths illustrates that the upper and lower faces become thicker and the core thickness becomes thinner. However, at shallow-to-moderate depths, it is recommended to use sandwich composite with a thick core to resist the shell buckling of composite submarine pressure hull. Full article