Abstract

Abstract

A fully geometric and constitutive nonlinear model for the description of the dynamic behavior of beam structures is developed. The
proposed formulation is based on the geometrically exact formulation for beams due to Simo but, in this article an intermediate curved
reference configuration is considered. The resulting deformation map belongs to a nonlinear differential manifold and, therefore, an
appropriated version of Newmark’s scheme is used in updating the kinematics variables. Each material point of the cross-section is
assumed to be composed of several simple materials with their own constitutive laws. The mixing rule is used to describe the resulting
composite. An explicit expression for the objective measure of the strain rate acting on each material point is deduced in this article.
Details about its numerical implementation in the time-stepping scheme are also addressed. Viscosity is included at the constitutive level by means of a thermodynamically consistent visco damage model developed in terms of the material description of the First Piola Kirchhoff stress vector. The constitutive part of the tangent tensor is deduced including the effect of rate dependent inelasticity. Finally, several numerical examples, validating the proposed formulation, are given.

Abstract

In this work, the nonlinear dynamic response of RC buildings with energy dissipating devices is studied using advanced computational techniques. A fully geometric and constitutive nonlinear model is used for describing the dynamic behavior of structures. The equations of motion are expressed in terms of cross sectional forces and strains and its weak form is solved using the displacement based finite element method. A suitable version of Newmark’s scheme is used in updating the kinematics variables in a classical Newton type iterative scheme. Material points of the cross section are assumed to be composed of several simple materials with their own constitutive laws. The mixing theory is used to treat the resulting composite. A specific finite element based on the beam theory is proposed for the dissipators including constitutive relations. Finally, several numerical tests are carried out to validate the proposed model.

Abstract

This work 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. Hydrokinetic turbines bring newer advantages and greater possibilities for green hydroelectric power generation. For this reason, achieving a very high lift blade rotor to take the maximum kinetic energy advantage for rivers with a slow velocity flow is very important. A very low inertia rotor permits a self-starting effect for the axial water flow turbine to take the maximum advantage of the river kinetic energy which is very important in this kind of devices. A turbine rotor hydrofoil made in composite material can be designed for this purpose. One of the most commonly used composite material analysis formulation is herein introduced. Specifically, a particular Serial/Parallel (S/P) Mixing Theory with a better relation between model accuracy vs. computational cost is provided. In front to other formulation, the S/P Mixing Theory not increasing the degrees of freedom of the problem because is a constitutive formulation. A brief introduction to fluid-dynamic concept involving in the analysis of a rotor of this type of turbines is presented. This allows seeing the origin of the actions applied to the rotor of this type of turbines. In addition, two simple examples that show the potentiality of the model are presented in this chapter. Then, an application to the design of a rotor blade of a passing turbine, made of carbon fiber-reinforced matrix composite material, is shown.

Abstract

An optimization method to identify the material parameters of composite structures using an inverse method is proposed. This methodology compares experimental results with their numerical reproduction using the finite element method in order to obtain an estimation of the error between the results. This error estimation is then used by an evolutionary optimizer to determine, in an iterative process, the value of the material parameters which result in the best numerical fit. The novelty of the method is in the coupling between the simple genetic algorithm and the mixing theory used to numerically reproduce the composite behavior. The methodology proposed has been validated through a simple example which illustrates the exploitability of the method in relation to the modeling of damaged composite structures.

Abstract

Abstract

A geometrically non‐linear formulation for composites and the resulting explicit dynamic finite element algorithm are presented. The proposed formulation assumes that small elastic and large plastic strains, being the anisotropy considered using tensors which map the model variables at each time step into an equivalent isotropic space, where the integration of the rate constitutive equations is performed. The evolution of the internal variables is calculated in the auxiliary spaces, taking into account the material non‐linear behaviour, and the results mapped back to the real stress space. The updating of the mapping tensors for each new spatial configuration allows the treatment of general anisotropic materials under large strain and can be extended to treat multiphase composite materials using the mixing theory. The behaviour of the composite is dictated by the mechanical response of each substance, and the resultant model allows a fully non‐linear analysis combining different material models, such as damage in one compounding substance, elastoplastic behaviour in the other, while a third substance behaves elastically.