Liz G. Nallim

A general algorithm for the study of the dynamical behaviour of beams

Abstract This paper presents a simple, accurate and flexible general algorithm for the study of a great number of beams vibration problems. The approach is developed based on the Rayleigh–Ritz method with characteristic orthogonal polynomial shape functions. It allows the inclusion of a number of complicating effects such as varying cross-sections, presence of an arbitrarily placed concentrated mass, ends elastically restrained against rotation and translation and presence of an axial, tensile force. Several cases are treated to show the simplicity and great flexibility of this approach, in the determination of frequencies. To demonstrate the accuracy of the present approach natural frequency coefficients are given for beams, from which comparison results are available. New results are also given for tapered beams with several complicating effects.

An enriched macro finite element for the static analysis of thick general quadrilateral laminated composite plates

ABSTRACT This article presents the formulation of an enriched macro finite element based on the trigonometric shear deformation theory for the static analysis of symmetrically laminated composite plates. Shear correction factor is not required because this theory accounts for tangential stress-free boundary conditions on the plate boundary surfaces. The macro element is obtained using the principle of virtual work and Gram-Schmidt orthogonal polynomials as enrichment functions. The implementation of the obtained algorithm is simple and efficient, and allows studying general quadrilateral plates with a single macro element. Several examples are presented to show the capability and applicability of the developed formulation.

Natural frequencies of edge restrained tapered isotropic and orthotropic rectangular plates with a central free hole

Abstract Natural frequencies of tapered orthotropic rectangular plates with a central free hole and edges restrained against rotation and translation are studied by using orthogonal polynomials in the Rayleigh–Ritz method and applying a generalization of the Rayleigh–Schmidt method. The two methods are quite general and can be used to study plates with any combinations of boundary conditions, taper and geometric parameters. To demonstrate the accuracy of the present approach natural frequency coefficients are given for isotropic plates with a central free hole, from which comparison results are available. New results are also given for orthotropic plates with several complicating effects. The studied problems are of interest in several field of engineering, since holes are present in plates due to operational conditions.

An inverse approach for the mechanical characterisation of vascular tissues via a generalised rule of mixtures

Mechanical factors such as stresses and strains play a major role in the growth and remodelling of soft biological tissues. The main constituents of tissue undergo different processes reacting to mechanical stimulus. Thereby, the characterisation of growth and remodelling requires an accurate estimation of the stresses and strains of their main components. Many soft tissues can be considered as composite materials and can be analysed using an appropriate rule of mixtures. Particularly, arterial tissue can be modelled as an isotropic soft matrix reinforced with preferentially oriented collagen fibres. An inverse approach to obtain the mechanical characterisation of each main component is proposed in this work. The procedure is based on a rule of mixtures raised in a finite deformation framework and generalised to include kinematics and compatibility equations for serial–parallel behaviour. This methodology allows obtaining the stress–strain relationship of the components fitting experimental data.

2.9 Composite Materials

This chapter presents the composite materials applied to water current turbine (WCT) hydrokinetic turbines. Here will be briefly described the features of these turbines, the fluid-dynamic behavior of the rotor, and its structure formed into a composite material. From the structural viewpoint an advanced composite material formulation that allows an appropriate structural design is introduced. The generalized composite formulations here introduced take into account the nonlinear mechanical behavior of the component materials (matrix and fiber), as the local behavior of plasticity and damage, its anisotropy, the fiber–matrix debonding, its material composition via a general mixing theory, and also the homogenized structural damage index definition.