António Pinto da Costa - Academia.edu (original) (raw)

Uploads

Papers by António Pinto da Costa

Meccanica, 2019

The numerical solution of the steady-state response of a uniform taut string on visco-elastic sup... more The numerical solution of the steady-state response of a uniform taut string on visco-elastic support under a concentrated transverse moving load is addressed. By recasting the governing second-order differential equation as a first-order system in convected coordinate, a local Discontinuous Least-Squares Finite Element Method (DLSFEM) formulation is developed within a complex-valued function space, to overcome numerical instabilities linked to high-velocity loads and handle far-field conditions through an effective Perfectly Matched Layer (PML) implementation. As an original advancement of the present DLSFEM-PML formulation, a coercivity theorem is proven for any first-order ordinary differential system and uniform error estimates are established for the finite element approximation for both L 2-and H 1-norms. Thus, the formulation newly joins a DLSFEM approach and a PML implementation, for solving the above-mentioned moving load problem. Numerical examples illustrate feasibility and accuracy of the method in reproducing the expected trends of solution and a priori error estimates.

International Journal of Solids and Structures, 2018

Universal analytical solution of the steady-state response of an infinite beam on a Pasternak ela... more Universal analytical solution of the steady-state response of an infinite beam on a Pasternak elastic foundation under moving load,

In this paper, a concept of “dynamic stability of quasi-static paths” is discussed that takes int... more In this paper, a concept of “dynamic stability of quasi-static paths” is discussed that takes into account the existence of fast (dynamic) and slow (quasi-static) time scales. It is essentially a continuity property with respect to the smallness of the initial perturbations (as in Lyapunov stability) and to the smallness of the quasi-static loading rate (that plays the role of the small parameter in singular perturbation problems). Three mechanical examples are presented that illustrate the similarities, the differences and the relations between this concept of "dynamic stability of quasi-static paths" and the one of Lyapunov stability of some related equilibrium configurations or dynamic trajectories.

In the present work we study some local characteristics of quasi-static trajectories of finite di... more In the present work we study some local characteristics of quasi-static trajectories of finite dimensional plane systems in unilateral contact with friction. An important tool for this study, in the neighborhood of an equilibrium state, is the computation of the solution set of the first order quasi-static rate problem. Theoretical results on existence/uniqueness of solution of the rate problem are presented in [1]. The rate problem has a mathematical structure similar to that of a dynamic problem studied in [2], and is formulated here as a Generalized Linear Complementarity Problem (GLCP) of dimension proportional to the number of particles currently in contact: each particle in contact with no reaction contributes with six variables to the dimension of the GLCP, while each particle in impending slip contributes only with two. The set of solutions of the rate problem is then computed by using the algorithm of De Moor [3]. This is a non-iterative algorithm that finds all solutions, ...

Solid Mechanics and its Applications, 1999

Journal of Sound and Vibration, 2015

The present paper is concerned with the behaviour of finite elastic beams, acted by a moving tran... more The present paper is concerned with the behaviour of finite elastic beams, acted by a moving transverse concentrated load, interacting with elastic foundations of different stiffnesses in compression and in tension. Using finite element analyses, the displacement amplitudes and the critical velocities of the load on a UIC-60 rail are computed and their dependence with respect to the difference between the foundation's moduli in compression and in tension is evaluated. The limit case of a tensionless foundation is as well analyzed. The numerical algorithm relies on the internal force vectors and tangent stiffness matrices computed exactly with automatic symbolic manipulation.

Journal of Engineering Mechanics, 1996

International Journal of Engineering Science, 2012

ABSTRACT In this paper, a concept of “stability of quasi-static paths” that takes into account th... more ABSTRACT In this paper, a concept of “stability of quasi-static paths” that takes into account the existence of fast (dynamic) and slow (quasi-static) time scales is discussed. It is essentially a continuity property with respect to the smallness of the initial perturbations (as in Liapunov stability) and to the smallness of the quasi-static loading rate (that plays the role of the small parameter in singular perturbation problems). Three mechanical examples are presented that illustrate the similarities, the differences and the relations between this concept of “stability of quasi-static paths” and the one of Liapunov stability of some related equilibrium configurations or dynamic trajectories.

Computers & Structures, 2004

ABSTRACT This paper deals with two related phenomena that may occur in frictional contact problem... more ABSTRACT This paper deals with two related phenomena that may occur in frictional contact problems: bifurcations in quasi-static paths and instability of equilibrium states. We will focus on the numerical computation of solutions of the problems that can capture those phenomena: the rate problem and the directional instability problem.

Computational Optimization and Applications, 2008

Journal of Applied Mechanics, 2011

This paper studies the friction induced vibrations that may develop in the neighborhood of steady... more This paper studies the friction induced vibrations that may develop in the neighborhood of steady sliding states of elastic orthotropic half-spaces compressed against a rigid plane moving tangentially with a prescribed speed. These vibrations may lead to flutter instability associated to a surfacelike oscillation. The system of dynamic differential equations and boundary conditions that governs the small plane oscillations of the half-space about the steady sliding state is established. The general form of the surface solutions to the plane strain case is given. The way how the coefficient of friction varies with changes in some of the system’s parameters is investigated. It is shown that for certain combinations of material data, low coefficients of friction are found for surface flutter instability (lower than in the isotropic case).

Impact And Friction Of Solids, Structures And Intelligent Machines, 2000

ABSTRACT

Advances in Mechanics and Mathematics, 2004

In this paper we revisit the quasi-static rate and the quasi-static evolution problems for finite... more In this paper we revisit the quasi-static rate and the quasi-static evolution problems for finite dimensional nonlinear elastic systems, in frictional contact with curved obstacles. Our objectives are: (i) to present complementarity formulations for the quasi-static rate problemj (ii) to discuss conditions for existence and uniqueness of solution for that problemj (iii) to present a differential inclusion formulation and related mathematical results for the quasi-static evolution problemj (iv) to present numerical results for a specific finite element example of (non-) uniqueness of solution for the quasi-static rate problem.

Computers & Structures, 2020

This paper concerns a computational implementation for solving a Moving Load (ML) problem on an i... more This paper concerns a computational implementation for solving a Moving Load (ML) problem on an infinite Euler-Bernoulli elastic beam on a Pasternak visco-elastic support. A steady-state dynamic response in convected coordinate is sought, by a numerical approach with discretization over a finite domain, implying spurious boundary reflections of non-evanescent waves. This is effectively solved by: (a) analytically formulating a new, true Perfectly Matched Layer (PML) approach, toward handling the underlying fourth-order differential problem and the corresponding far-field conditions, without adopting special boundary conditions; (b) outlining a local Discontinuous Least-Squares Finite Element Method (DLSFEM) formulation, apt to provide a robust approach for the present non self-adjoint problem and to conveniently handle the jump condition in the shear force at the concentrated ML position. Consistent numerical results are illustrated and compared to an available analytical solution, showing a perfect match, with a complete removal of spurious boundary effects and a proof of theoretical a priori error estimates. Further results are produced for a case with multiple MLs. The paper shows that the present innovative DLSFEM-PML formulation is effectively suitable to numerically solve a steady-state ML problem on an infinite beam, setting up a new computational tool in such a challenging mechanical context.

Acta Mechanica, 2018

The present paper is concerned with the numerical modelization of the transient dynamic response ... more The present paper is concerned with the numerical modelization of the transient dynamic response of a simply supported Euler-Bernoulli elastic beam resting on a Winkler-type foundation, under the action of a transverse concentrated load, moving at a constant velocity along the beam, displaying an harmonicvarying magnitude in time. The elastic foundation, assumed as homogeneous in space, behaves according to a bilinear constitutive law, characterized by two different stiffness coefficients in compression and in tension. A finite element method approach coupled with a direct integration algorithm is developed for efficiently tracing the nonlinear dynamic response of the beam-foundation system. An original automated procedure is set, as being apt to resolve all required space/time discretization issues. Extensive parametric numerical analyses are performed to investigate how the frequency of the harmonic moving load amplitude and the ratio between the foundation's moduli in compression and in tension affect the so-called critical velocities of the moving load, leading to high transverse beam deflections. Analytical interpolating expressions are proposed and fitted for the achieved two-branch critical velocity trends. The present outcomes shall reveal potential practical implications in scenarios of contemporary railway engineering, especially in terms of lowering down the admissible highspeed train velocities, as for structural requirement or preventing potential passenger discomfort.

European Journal of Mechanics - A/Solids, 2018

This paper presents a study on the dynamic response of beams on elastic foundations, subjected to... more This paper presents a study on the dynamic response of beams on elastic foundations, subjected to a uniformly moving oscillator. Using a finite element model programmed within a MATLAB environment the response of the system is studied for three different types of mechanical behaviour of the foundation: (a) linear elastic (classical Winkler model), (b) nonlinear elastic (in which the foundation reaction displays a cubic dependence on the beam displacement) and (c) bilinear elastic (with different compressive and tensile stiffnesses). The effects of the oscillator's natural frequency and velocity and of the foundation's stiffness and damping are investigated. In particular, critical velocities of the oscillator and ranges of velocities for which the system is dynamically unstable are numerically determined for the first time in the above mentioned nonlinear cases.