Geometric Non Linear Analysis of Composite Shells Under Thermomechanical Loading

This paper provides information on hyperboloids of revolution surfaces and their classification, using methods of differential geometry and computer design. All surfaces are plotted by means of computer graphics. The geometric nonlinear numerical analysis of thin shells in the form of hyperboloid of revolution surfaces on buckling resistance and stress-strain state is given in this paper, using the finite elements method in a computer software. Comparison is done with the result of the finite elements linear analysis of their buckling resistance.

State-of-the-art nonlinear computational analysis of shells, nonlinearities due to large deformations and nonlinear material behavior, alternative shell element formulations, algorithms and implementational aspects, composite and sandwich shells, local and global instabilities, optimization of shell structures and concepts of shape finding methods of free from shells. Furthermore, algorithms for the treatment of the nonlinear stability behavior of shell structures (including bifurcation and snap-through buckling) are presented in the book.

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

Finite- and boundary-element linear and nonlinear analyses of shells and shell-like structures: A bibliography (1999–2001)

Geometrically non-linear analysis of arbitrary elastic supported plates and shells using an element-based Lagrangian shell element

Procedures are investigated by which nonlinear finite element shell analysis algorithms can be simplified to provide more cost effective approximate analyses of orthogonally-reinforced concrete flat plate structures. Two alternative effective stiffness formulations, and an unbalanced force formulation, are described. These are then implemented into a nonlinear shell analysis algorithm. Nonlinear geometry, three-dimensional layered stress analyses, and other general formulations are bypassed to reduce the computational burden. In application to standard patch test problems, these simplified approximate analysis procedures are shown to provide reasonable accuracy while significantly reducing the computational effort. Corroboration studies using various simple and complex test specimens provide an indication of the relative accuracy of the constitutive models utilized. The studies also point to the limitations of the approximate formulations, and identify situations where one should revert back to full nonlinear shell analyses.

Geometrically nonlinear analysis of laminate composite plates and shells using the eight-node hexahedral element with one-point integration

Nonlinear large deformation analysis of shells using the variational differential quadrature method based on the six-parameter shell theory

In this paper, a mixed spline boundary element and finite element method is suggested to analyse non-linear bending of plates and shells. Only the fundamental solutions for plates are required in order to establish the boundary integral equations. A quadratic rectangular spline element is adopted to deal with the membrane effects of plates and shells. Numerical examples show that the approach developed in this paper is very effective and especially promising for the non-linear analysis of plates and shells.

A refined non-conforming triangular plate/shell element for linear and geometrically nonlinear analysis of plates and shells is developed in this paper based on the refined non-conforming element method (RNEM). A conforming triangle membrane element with drilling degrees of freedom in Cartesian coordinates and the refined non-conforming triangular plate-bending element RT9, in which Kirchhoff kinematic assumption was adopted, are used to construct the present element. The displacement continuity condition along the interelement boundary is satisfied in an average sense for plate analysis, and the coupled displacement continuity requirement at the interelement is satisfied in an average sense, thereby improving the performance of the element for shell analysis. Selectively reduced integration with stabilization scheme is employed in this paper to avoid membrane locking. Numerical examples demonstrate that the present element behaves quite satisfactorily either for the linear analysis of plate bending problems and plane problems or for the geometrically nonlinear analysis of thin plates and shells with large displacement, moderate rotation but small strain.

A local–global FE model for nonlinear analysis of column-supported shells of revolution

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.

A theory is presented to predict the influence of non-linearities associated with the wall of the shell and with the fluid flow on the dynamic of elastic, thin, orthotropic open and closed cylindrical shells submerged and subjected to an internal and external fluid. The open shells are assumed to be freely simply-supported along their curved edges and to have arbitrary straight edge boundary conditions. The method developed is a hybrid of thin shell theory, fluid theory and the finite element method. The solution is divided into four parts. In part one, the displacement functions are obtained from Sanders’ linear shell theory and the mass and linear stiffness matrices for the empty shell are obtained by the finite element procedure. In part two, the modal coefficients derived from the Sanders-Koiter non-linear theory of thin shells are obtained for these displacement functions. Expressions for the second and third order non-linear stiffness matrices of the empty shell are then determined through the finite element method. In part three a fluid finite element is developed, the model requires the use of a linear operator for the velocity potential and a linear boundary condition of impermeability. With the non-linear dynamic pressure, we develop in the fourth part three non-linear matrices for the fluid. The non-linear equation of motion is then solved by the fourth-order Runge-Kutta numerical method. The linear and non-linear natural frequency variations are determined as a function of shell amplitudes for different cases.

Nonlinear analysis of FG-sandwich plates and shells

The nonlinear analysis of thin-walled shells is not a rarity, particularly the nonlinear strength one. Many works are devoted to linear and nonlinear analyses of shells of classical form: cylindrical, spherical, hemispherical, shallow, conical. The concept of shells of complex geometry appears when the coefficients of the first and second quadratic forms of their middle surfaces are functions of the curvilinear coordinates. Concerning nonlinearity, it is generally accepted that four different sources of nonlinearity exist in solid mechanics: the geometric nonlinearity, the material nonlinearity and the kinetic nonlinearity. The above theoretical aspect of the nonlinearity, applied to a sinusoidal velaroidal shell with the inner radius r0=1m, the outer radius R=20m and the number of waves n= 8, will give rise to the investigation of its nonlinear buckling resistance. The building material is a concrete. The investigation emphasizes more on the material and the geometric nonlinearities, which are more closed to the reality. Finite element model of the shell consists of 6400 elements and 3280 nodes, the total number of nodal unknown - 18991. For surface modelling was used flat shell elements with six degrees of freedom in the node. The boundary conditions cor- respond to hinged bearing on the outer and inner contours. The result of the investigation is the buckling force of the shell under self-weight and uniformly vertically distributed load on its area, the corresponding numerical values of displacements and the buckling mode