Laminated Beam Analysis by Polynomial, rigonometric, Exponential and Zig-Zag Theories

A number of refined beam theories are discussed in this paper. These theories were obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor's polynomials, trigonometric series, exponential, hyperbolic and zig-zag functions. The Finite Element method is used to derive governing equations in weak form. By using the Unified Formulation introduced by the first author, these equations are written in terms of a small number of fundamental nuclei, whose forms do not depend on the expansions used. The results from the different models considered are compared in terms of displacements, stress and degrees of freedom (DOFs). Mechanical tests for thick laminated beams are presented in order to evaluate the capability of the finite elements. They show that the use of various different functions can improve the performance of the higher-order theories by yielding satisfactory results with a low computational cost

Structural-Electrical-Coupled Formulation for the Free Vibration of a Piezoelectric-Laminated Plate Using the Analytical Arbitrary Quadrilateral p

An analytical quadrilateral p element is developed for solving the free vibrations of piezoelectric-laminated plates. The formulations of the displacement and strain fields are based on first-order shear deformation plate theory. The coupling effect between the electrical and stress fields is also considered. The Legendre orthogonal polynomials are used as the element interpolation functions, and the analytical integration technique is adopted. It is found that the present p element method gives high numerical precision results, fast and monotonic convergence rate. In the numerical cases, the effects of the number of hierarchical terms and mesh size on the convergence rate are investigated. Examples of square plates with different displacement and potential boundary conditions are studied. In the comparisons, the solutions of the present element are in good agreement with those obtained from other classical and finite element methods

Dynamic Fracture in Thin Shells Using Meshfree Method

We present a meshfree approach to model dynamic fracture in thin structures. Material failure is modeled based on a stress-based criterion and viscoplastic is used to describe the material behavior in the bulk material. Material fracture is simply modeled by breaking bonds between neighboring particles. The method is applied to fracture of cylindrical thin structures under explosive loading. The loading is modelled by a pressure-time history. Comparisons between the computational results and experimental data illustrate the validity and robustness of the proposed method

Isogeometric analysis based on rational splines over hierarchical T-mesh and alpha finite element method for structural analysis

This thesis presents two new methods in finite elements and isogeometric analysis for structural analysis. The first method proposes an alternative alpha finite element method using triangular elements. In this method, the piecewise constant strain field of linear triangular finite element method models is enhanced by additional strain terms with an adjustable parameter a, which results in an effectively softer stiffness formulation compared to a linear triangular element. In order to avoid the transverse shear locking of Reissner-Mindlin plates analysis the alpha finite element method is coupled with a discrete shear gap technique for triangular elements to significantly improve the accuracy of the standard triangular finite elements. The basic idea behind this element formulation is to approximate displacements and rotations as in the standard finite element method, but to construct the bending, geometrical and shear strains using node-based smoothing domains. Several numerical examples are presented and show that the alpha FEM gives a good agreement compared to several other methods in the literature. Second method, isogeometric analysis based on rational splines over hierarchical T-meshes (RHT-splines) is proposed. The RHT-splines are a generalization of Non-Uniform Rational B-splines (NURBS) over hierarchical T-meshes, which is a piecewise bicubic polynomial over a hierarchical T-mesh. The RHT-splines basis functions not only inherit all the properties of NURBS such as non-negativity, local support and partition of unity but also more importantly as the capability of joining geometric objects without gaps, preserving higher order continuity everywhere and allow local refinement and adaptivity. In order to drive the adaptive refinement, an efficient recovery-based error estimator is employed. For this problem an imaginary surface is defined. The imaginary surface is basically constructed by RHT-splines basis functions which is used for approximation and interpolation functions as well as the construction of the recovered stress components. Numerical investigations prove that the proposed method is capable to obtain results with higher accuracy and convergence rate than NURBS results

A study on the behavior of laminated and sandwich composite plates using a layerwise theory

The numerical study of structures constituted from composite materials, regardless the underlying shear deformation theory used may be framed into an equivalent single-layer or a layerwise methodology. The adoption of one of these approaches is mainly ruled by the detail one needs to put in the description of the deformation kinematics and on the subsequent description of other relevant quantities such as stresses or frequencies. Being important to address both qualitative and quantitatively the influence of different parameters involved in the models and materials used to represent a structure, it is also relevant to understand how layerwise theories can predict its static and dynamic response. These different issues may be addressed by carrying out parametric studies to characterize the influence of specific parameters on the mechanical performance of sandwich and laminated composite plates. To this purpose a layerwise theory based on the first order shear deformation theory, is considered, and a set of different test cases are analyzed in light of this approach, providing results which may also be useful for later comparison purposes