An effective meshfree reproducing kernel method for buckling analysis of cylindrical shells with and without cutouts

Free Vibrations of Composite Shallow Circular Cylindrical Shell Panels Stiffened by A Bonded Non-Central Shell Strip

Dynamic analysis of shallow shells with a doubly-curved triangular finite element

Boundary Element Analysis of Cracks in Shear Deformable Plates and Shells. Topics in Engineering, Vol 43

A meshless local Petrov‐Galerkin (MLPG) formulation is presented for analysis of shear deformable shallow shells with orthotropic material properties and continuously varying material properties through the shell thickness. Shear deformation of shells described by the Reissner theory is considered. Analyses of shells under static and dynamic loads are given here. For transient elastodynamic case the Laplace‐transform is used to eliminate the time dependence of the field variables. A weak formulation with a unit test function transforms the set of the governing equations into local integral equations on local subdomains in the plane domain of the shell. The meshless approximation based on the Moving Least‐Squares (MLS) method is employed for the implementation.

Geometrically nonlinear analysis of shallow shells using higher order finite elements

A sound variational framework applicable to shallow shell analysis is proposed in this work. Addition of so-called drilling degrees of freedom, usually absent in the shell analysis, is facilitated within the proposed framework at the continuum level. Therefore, it provides a solid theoretical basis for development of thick and thin curved shell elements with six degrees of freedom per node.

The purpose of the paper is to study stability and free vibrations of laminated plates and shallow shells composed of functionally graded materials. The approach proposed incorporates the Ritz method and the R-functions theory. It is assumed that the shell consists of three layers and is loaded in the middle plane. The both cases of uniform as well as non-uniform load are possible. The power-law distribution in terms of volume fractions is applied to get effective material properties for the layers. These properties are calculated for different arrangements and thicknesses of the layers by the analytical formulae obtained in the paper. The mathematical formulation is carried out in framework of the first-order shear deformation theory. The proposed approach consists of two steps. The first step is to define the pre-buckling state by solving the respective elasticity problem. The critical buckling load and frequencies of functionally graded material shallow shells are determined in the second step. The highlight of the method proposed is that it can be used for vibration and buckling analysis of plates and shallow shells of complex shape. The numerical results for frequencies and buckling load of plates and shallow shells of complex shape and different curvatures are presented to demonstrate the potential of the method developed. Different functionally graded material plates and shallow shells composed of a mixture of metal and ceramics are studied. The effects of the power law index, boundary conditions, thickness of the core, and face sheet layers on the fundamental frequencies and critical loads are discussed in this paper. The main advantage of the method is that it provides an analytical representation of the unknown solution, which is important when solving nonlinear problems.

For certain continuum problems, it is desirable and beneficial to combine two different methods together in order to exploit their advantages while evading their disadvantages. In this paper, a bridging transition algorithm is developed for the combination of the meshfree method (MM) with the finite element method (FEM). In this coupled method, the MM is used in the sub-domain where the MM is required to obtain high accuracy, and the FEM is employed in other sub-domains where FEM is required to improve the computational efficiency. The MM domain and the FEM domain are connected by a transition (bridging) region. A modified variational formulation and the Lagrange multiplier method are used to ensure the compatibility of displacements and their gradients. To improve the computational efficiency and reduce the meshing cost in the transition region, regularly distributed transition particles, which are independent of either the meshfree nodes or the FE nodes, can be inserted into the transition region. The newly developed coupled method is applied to the stress analysis of 2D solids and structures in order to investigate its’ performance and study parameters. Numerical results show that the present coupled method is convergent, accurate and stable. The coupled method has a promising potential for practical applications, because it can take advantages of both the MM and FEM when overcome their shortcomings.

Correction of stiffness and mass matrices utilizing simulated measured modal data

Shell structures are widely used in various fields of technology and construction. Often, they play the role of a bearing surface with assemblies, overlays, and aggregates installed on them. At the same time, in solving various problems, such attached elements are considered as the elements concentrated at the points and rigidly connected. Vibrations of an orthotropic viscoelastic shallow shell with concentrated masses in a geometrically nonlinear setting are considered. The equation of motion for a shallow shell is derived based on the Kirchhoff-Love theory. The traditional Boltzmann-Volterra theory is used to describe the viscoelastic properties of a shallow shell. The effect of concentrated masses is taken into account using the Dirac delta function. Using the polynomial approximation of the deflections of the Bubnov-Galerkin method, the problem is reduced to solving a system of ordinary nonlinear integro-differential equations with variable coefficients. In the calculations, the three-parameter Koltunov-Rzhanitsyn kernel was used as a weakly singular relaxation kernel. A numerical method was used to solve the resulting system that eliminates the singularity in the relaxation kernel. The problem of nonlinear vibrations of an orthotropic viscoelastic shallow shell with concentrated masses is solved. The influence of concentrated masses and location, properties of the shell material, and other parameters on the amplitude-frequency response of the shallow shell vibrations is investigated.

Coupling of the meshfree and finite element methods for determination of the crack tip fields

Incremental analysis of axisymmetric shallow shells with varying strain-displacement equations

This study deals with the geometrically non-linear vibration analysis of concrete shallow funicular shells of rectangular plan with four clamped edges under impulse loads. The shape of a concrete funicular shell is such that the shell is subjected to pure compression under its dead weight. Following the existing method presented for the linear vibration analysis, the geometrically non-linear vibration analysis is considered through the use of non-linear shallow shells theory. Each displacement component is expanded in a double Fourier series and the kinetic energy, the elastic strain energy and the virtual work done by external forces are calculated in terms of the displacement components. Then, the equations of motion are obtained using the Lagrangian approach and are solved with the Runge–Kutta fourth-order method. The solution is verified against the results obtained with the finite-element method. The difference between the results of the linear and non-linear vibration analyses has been considered. Furthermore, it is indicated that under the considered dynamic loads, internal moments and consequentially tensile stresses are formed in the funicular shell and the shell does not behave purely as a funicular element. Finally, the plan aspect ratio effect on the time response of funicular shells has been shown.

SummaryThe Field/Boundary Element method is used to solve problems involving static and dynamic analysis of thin elastic plates and shallow shells undergoing finite delections. The method is developed through the use of the weak form of the appropriate governing differential equations and boundary conditions. The resulting equations are then linearized and incremental solution strategies are discussed. In the case of problems involving limit points, a procedure which is a variation of an arc-length method is described. Numerical results of both plate and shallow shell problems are given to demonstrate the computational efficiency of the method.

Nonlinear axisymmetric buckling analysis of the FGM sandwich shallow spherical shells under thermomechanical loads