Failure mode analysis of cylindrical sandwich shells with truss core considering shell/core debonding under bending/compressive loading

In this study, a high-order model for the analysis of circular cylindrical composite sandwich shells subjected to low-velocity impact loads is presented. The sandwich shell is composed of two composite face sheets and a transversely compliant core. The impact behavior of the cylindrical composite sandwich shells is described by a high-order sandwich shell theory. The interaction between the impactor body and the sandwich shell is approximated using a spring mass model. The present analysis is based on an iteration procedure, and yields analytic functions describing the contact force history. The contact force is considered to be distributed uniformly over a contact patch, the size of which depends on the magnitude of the impact load as well as the elastic properties and geometry of the impactor. Finally, the obtained results have been compared with the available experimental results, and a good correlation has been found.

Failure maps and optimal design of metallic sandwich panels with truss cores subjected to thermal loading

Nonlinear analysis of cylindrical sandwich shells with porous core and CNT reinforced face-sheets by higher-order thickness and shear deformation theory

Analysis of FGM micro cylindrical shell with variable thickness using Cooper Naghdi model: Bending and buckling solutions

A higher-order theory for the analysis of cylindrical and conical sandwich shells with flexible core is presented. The formulation is based on a three-layer sandwich model. The governing equations and the boundary conditions of each individual layer are derived according to the principle of minimum total potential energy. With the consideration of the continuity of the displacements and the internal stress fields at the interfaces, the governing partial differential equations for the sandwich shell are achieved. They are reduced into ordinary differential equations using Fourier decomposition and then solved through a numerical integration procedure. The theory is verified by comparison of achieved results to those published in the literature and to finite element computations.

This paper focuses on the vibration and damping analysis of three-layered sandwich cylindrical shells with stiff composite face layers and a viscoelastic core. The equations of motion and boundary conditions governing the free vibration are derived by using the Hamilton’s principle. Then, generalized differential quadrature method is used to solve these equations to obtain the natural frequencies and modal loss factors. Results are validated against the ones that already exist in the literature and performed finite element method analyses of current study. In addition, a parametric study is performed for a sandwich shell with carbon fiber–reinforced plastic face layers and a frequency-dependent viscoelastic core. A 10-parameter fractional derivative model is used to represent the viscoelastic behavior of the core layer. The effects of system parameters, that is, layer thicknesses, the orientation angle of the face layers, and the subtended angle on the vibration and damping characteristics of open cylindrical shells, are investigated in detail. The vibration and damping analyzes of sandwich shells with frequency-dependent viscoelastic core are performed for the first time to the best of the authors’ knowledge.

The sandwich structures are three- or multilayered structures such that their mechanical properties are better than each single layer. In the current research, a three-layered cylindrical shell including a functionally graded porous core and two reinforced nanocomposite face sheets resting on the Pasternak foundation is used as model to provide a comprehensive understanding of vibrational behavior of such structures. The core is made of limestone, while the epoxy is utilized as the top and bottom layers’ matrix phase and also it is reinforced by the graphene nanoplatelets (GNPs). The pattern of the GNPs dispersion and the pores distribution play a crucial role at the continuous change of the layers’ properties. The sinusoidal shear deformation shells theory and the Hamilton’s principle are employed to derive the equations of motion for the mentioned cylindrical sandwich shell. Ultimately, the impacts of the model’s geometry, foundation moduli, mode number, and deviatory radius on the vibrational behavior are investigated and discussed. It is revealed that the natural frequency and rotation angle of the sandwich shell are directly related. Moreover, mid-radius to thickness ratio enhancement results in the natural frequency reduction. The results of this study can be helpful for the future investigations in such a broad context. Furthermore, for the pipe factories current study can be effective at their designing procedure.

An asymptotic transfer function method is presented for modeling and analysis of conical shells. The displace- ment functions are first expanded in Fourier series in the circumferential direction, and the motion equations are decoupled into a group of partial differential equations with one space variable and one time variable. Introducing a small perturbation parameter and using the Laplace transformation and perturbation technique, the partial differential equations with variable coefficients are reduced to ordinary differential equations with constant co- efficients, which are solved by the transfer function method. The method is used to perform analysis of stepped conical shells with different conical angle or thickness and subjected to various initial and boundary conditions. Numerical methods are presented and compared with the finite element method. ONICAL shells have wide applications in aeronautic, astro- nautic, civil, and chemical engineering. The research on their mechanical behavior under various external excitations and bound- ary restrictions has great importance in engineering practice. As one type of revolutionary thin shells, conical shells have been studied by many researchers, and a lot of modeling and analysis methods have been developed. Chang1 gave a literature review of the vibration of conical shells. Liew2 reviewed recent developments in the free vibration analysis of thin, moderately thick shallow shells. Com- pared with cylindrical shells, conical shells are difficult to analyze in exact and closed form because of the mathematical complex- ity in geometry and variable surface curvature.2 Wan3-4 obtained a closed-form solution of the variable coefficient differential equa- tions of conical shells in terms of generalized hypergeometric func- tions. Tong5 obtained the solution of laminated conical shells in the form of power series. However, their solutions are very com- plicated and are difficult to use for complex loads, boundary con- ditions, and geometric configurations. Therefore, approximate or numerical methods, such as Raleigh-Ritz, Galerkin, finite differ- ence, and finite element methods, have been widely used in the analyses. Teichmann6 presented an approximate solution of funda- mental frequencies and buckling loads of cylindrical and conical shell panels. Srinivasan and Krishnan7 provided the free vibration frequencies of fully clamped open conical shells by using an inte- gral equation approach. Cheung et al.8 employed a spline finite strip method to investigate the natural frequencies of fully clamped singly curved shells, and design charts for specific fully supported conical shell configurations were presented. Xi et al.9 studied free vibra- tion of composite shells of revolution by the finite element method. Sivadas and Ganesan10 conducted vibration analysis of laminated conical shells with variable thickness. These methods provide ef- fective ways for engineering analysis in most cases. However, their defaults are obvious in some specific situations, such as analysis concerned with stress concentration, high-frequency response, etc. Based on the method proposed in Refs. 11 and 12, an asymp- totic distributed transfer function method for the analysis of conical shells is presented in this paper. First, the displacements, external excitations, and boundary conditions are expanded in Fourier se- ries in a circumferential direction. Because of the orthogonality of trigonometric functions, the governing equations for different wave numbers are decoupled and Laplace transformation is used to transform the time t to obtain ordinary differential equations with complex parameter s. Second, introducing the perturbation pa- rameter £ = Lsma/r(), those ordinary differential equations with variable coefficients are reduced to a group of ordinary differential

Compression performances and failure maps of sandwich cylinders with pyramidal truss cores obtained through geometric mapping and snap-fit method

Axisymmetric static and frequency analyses of anisotropic cylindrical thin shells with one and two perfectly bonded ring piezoactuators are performed. The shell is assumed to be linear elastic and made of laminated composite materials. The electroelastic constitutive relations for the piezoelectric materials are also assumed to be linear. It is shown that, if there exists a special relationship involving the membrane and the membrane-bending coupling stiffness matrices, the analysis is greatly simplified. In such a situation, simple closed form solutions of the equilibrium equations are obtained for the case of an infinite shell with one or two actuators. Kirchhoff's assumptions are used for the analysis and the dynamic formulation is derived from a variational principle which includes the total structural potential energy and the electrical potential energy of the piezoelectric material, involving both mechanical and electrical variables. The finite element method is then applied to obtain the stiffness and mass matrices. The computer code developed to implement the formulation allows the static and dynamic analyses of arbitrary cylindrical shells with piezoelectric actuators. Good agreement is reached between the analytical solution found and the numerical procedure implemented. Results indicate that the maximum normalized displacement and its location vary according to the actuator length. Furthermore, a frequency analysis is carried out in a broad range of frequencies to investigate the effect of mass properties on the response of a simply supported cylindrical shell.

This paper presents a nonlinear high-order theory for cylindrical sandwich shells with flexible cores, extending a previously presented high-order theory for sandwich plates. The outer and inner faces are assumed to be relatively thin compared to the core and the effects from the core compressibility are addressed in the solution by incorporating the extended nonlinear core theory into the constitutive relations of the cylindrical shells. The governing equations and boundary conditions for the cylindrical shells are derived using a variational principle. Numerical results are presented for the cases where the two faces and the core are made of orthotropic materials. These results show that this model could capture the nonlinearity in the transverse stress distribution in the core of the cylindrical sandwich shell. Numerical results are presented on the details of the stress and displacement profiles for a cylindrical sandwich shell under localized external pressure. This study could have significance for the optimal design of advanced cylindrical sandwich shells.

In this paper, post buckling behavior of thin steel and aluminum cylindrical shells with rectangular cutouts under axial loading was studied experimentally and also using the finite element method. Riks method is used for analyzing the cylindrical shells. The effect of longitudinal and circumferential stiffeners (ribs and stringer) was studied on the buckling load and the post buckling behavior as the stiffeners used individually and in combination with each other. It was shown that by adding stringer, the buckling load improves and the rib has a positive effect on the post buckling behavior of the structure. Some tests were performed by ZwickRoell tensile/compression testing machine and it was carried out for both types of steel and aluminum shells with and without stiffeners. Comparing the experimental results with the FEA results shows good agreement. Nonlinear analysis of cylindrical steel and aluminum shells with cutout have demonstrated that, in some cases, a local buckling called snap-back can be seen in the load-displacement path. Snap-back which is a decrease in the amount of both load and displacement indicates this local buckling. This phenomenon is because of appearing mode shapes sequentially during the numerical buckling analysis of shells. Although these local buckling happened, the structure is still endured the higher loads.

This paper summarizes results obtained by the author and his associates and students over the last two decades on limit analysis and optimal plastic design of plates and cylindrical shells. Circular metal plates are first considered, including minimum weight plastic design. Rectangular plates are then treated, both in metal and reinforced concrete. Limit analysis of cylindrical metal shells with reinforcing rings is the next subject, followed by optimal design of such shells. It is concluded that computer-aided analytical methods remain of value to complement purely numerical approaches.

The present study deals with the vibration analysis of sandwich cylindrical shells with the functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets resting on elastic medium under internal pressure. Two FG-CNTRC face sheets along with homogeneous core are considered as the sandwich cylindrical shell. The overall mechanical properties of CNT-reinforced composites are presented in accordance to the refined rule of mixture. Based on the higher-order shear deformation theory (HSDT) and in the context of the variational differential quadrature (VDQ) method, the discretized version of governing equations is provided. Validation of the proposed model is demonstrated. Several numerical results are also represented to study the impacts of various material and geometrical factors on the vibration analysis of sandwich cylindrical shells. The results reveal that in the case of constant total thickness, increasing the core-to-face sheet thickness ratio decreases the dimensionless frequencies.

In this paper, semi-analytical and analytical methods for the nonlinear static and dynamic buckling analyses of imperfect functionally graded porous (FGP) cylindrical shells subjected to axial compression are presented. The structure is embedded within a generalized nonlinear elastic foundation, treated as a two-parameter Winkler–Pasternak foundation augmented by a nonlinear cubic stiffness. The material property of the shell changes continuously through the thickness. Two types of FGP distributions, i.e. uniform porosity distribution (UPD) and nonuniform porosity distribution (NPD), are considered. By applying the Galerkin’s method to the von Kármán equations, the buckling of the shells was solved. The fourth-order Runge–Kutta method is utilized to obtain the responses of nonlinear dynamic buckling (NDB). The results obtained for some special cases are compared with those available elsewhere. The effects of various geometrical properties, material parameters and elastic foundation coefficients are investigated on the nonlinear static buckling (NSB) and dynamic buckling (DB) analyses of the shells. It was shown that various types of porosity, imperfection and the elastic foundation parameters have a strong effect on the buckling behaviors of the FGP cylindrical shells.