Evandro Parente

Dynamic Viscoelastic Analysis of Asphalt Pavements using a Finite Element Formulation

ABSTRACT This paper studies the effect of time and load rate on the structural response of asphalt pavements when the surface layer is a linear viscoelastic material. A finite element incremental algorithm for dynamic analysis of viscoelastic solids is presented, where the stresses are computed using a hereditary integral in which the relaxation modulus is described by a Prony-Dirichlet series. The stresses are integrated in a semi-analytical form, whereas the dynamic equilibrium equations are integrated by the Trapezoidal Rule. Different pulse loads are considered and the viscoelastic responses of different asphalt layer thicknesses are compared. Several performance indicators typically utilized in pavement design are studied, particularly those at the surface layer, i.e., tensile stress and strain, shear strain, and surface deflection.

An Object-Oriented System for Finite Element Analysis of Pavements

The calculation of displacements, stresses and strains caused by vehicle loads in pavements is not a simple task even when considering all layers formed by linear elastic materials. In reality, surface and granular layers present a complex constitutive behavior, with nonlinear and time-dependent effects. Such effects should be considered in mechanistic pavement design methodologies which make use of the pavement structural response into specific distress models [1]. Today, there is a trend in the pavement academic community to substitute pavement analysis based on the Multilayer Elastic Theory by analysis based on the Finite Element Method — FEM [2].

Consideration of Structural Member Deformation Constraints Using Lagrange Multipliers

This paper is concerned with the analysis of framed structures with inextensible and rigid members, i.e., members without axial and bending strains. Rigid and inextensible members may be useful in educational software because they capture the essence of the structural behavior with a reduced the number of variables. In addition, they allow a comparison with results obtained by hand calculation using classical structural analysis methods. There are three main approaches to constraint handling: transformation, penalty function and Lagrange multiplier methods. The transformation methods do not allow the determination of axial forces in inextensible member or bending moments in rigid members. On the other hand, the penalty function method allows the computation of internal forces in constrained members and its implementation is simple. However, as the penalty factor increases, the stiffness matrix becomes increasingly ill-conditioned, which may lead to large solution errors. This paper presents a methodology for considering structural member deformation constraints using Lagrange multipliers. It consists of adding strain constraints into the total potential energy minimization, leading to a quadratic programming problem. In addition, this approach is very suitable for computational implementation because it does not affect the generic characteristic of a matrix structural analysis. The solution gives rise to one Lagrange multiplier per constraint, which is essential for computing member internal forces. However, there are situations in which inextensible and rigid member constrains may be redundant, which prevents the determination of dependent Lagrange multipliers. Although not implemented, a special treatment is indicated for the solution of this problem.