Papers by Philipe Almeida
Journal of the Brazilian Society of Mechanical Sciences and Engineering
SAÚDE PÚBLICA NO SÉCULO XXI, 2021
Proceedings of the XXXVIII Iberian Latin American Congress on Computational Methods in Engineering, 2017
The implementation of high-order (spectral) approximations associated with FEM is an approach to ... more The implementation of high-order (spectral) approximations associated with FEM is an approach to overcome the difficulties encountered in the numerical analysis of complex problems. This paper proposes the use of the spectral finite element method, originally developed for computational fluid dynamics problems, to achieve improved solutions for these types of problems. Here, the interpolation nodes are positioned in the zeros of orthogonal polynomials (Legendre, Lobatto, or Chebychev) or equally spaced nodal bases. A comparative study between the bases in the recovery of solutions to 1D and 2D elastostatic problems are performed. Examples are evaluated, and a significant improvement is observed when the SFEM, particularly the Lobatto approach, is used in comparison to the equidistant base interpolation.
Applied and Computational Mechanics, 2020
Due to the limitation that the classical beam theories have in representing transversal shear str... more Due to the limitation that the classical beam theories have in representing transversal shear stress fields, new theories, called high order, have been emerging. In this work, the principal high order theories are unified in single kinematics and applied to the Equivalent Single Layer Theory. The governing equations and the boundary conditions for laminated beams are consistent variational obtained. From the equilibrium equations, the high order spectral finite element model was developed using the polynomial functions of Hermite and Lagrange, with interpolants in the zeros of Lobatto's polynomials. Finally, to demonstrate the finite element model's outstanding efficiency, numerical results (static and dynamic) are shown and compared with the elasticity theory solution
Theoretical and Applied Fracture Mechanics, 2020
This work deals with the use of Boundary Element Method (BEM) formulations in fracture problems i... more This work deals with the use of Boundary Element Method (BEM) formulations in fracture problems in a 2D approach. BEM is a suitable method for solving this type of problem, since the absence of a domain mesh translates into a more efficient modeling of regions with high stress concentration. Besides, reducing the dimensionality of the mesh results in a convenient remeshing process. Regarding the nonlinear BEM formulation, an alternative to the classic dual formulation is used, with the introduction of an initial stress field to represent the cohesive zone, based on the concept of dipoles. This formulation is particularly interesting because it is able to represent mathematically the presence of the fracture process zone (FPZ) with only three algebraic equations (related to stress correction) per source point located in the crack path. In contrast, dual BEM formulation requires four algebraic equations (displacements and forces) per source point. As for the effects relevant to the nonlinear system, two distinct iterative solving algorithms are used, Constant Operator (CO) and Tangent Operator (TO). Only the elastic stiffness of the structure in the search of equilibrium point is considered in the first one, while the latter takes into account the mechanical degradation properties. Some examples are presented to validate the use of the Dipole BEM/TO formulation in crack propagation analysis and also in multiple crack analysis. Finally, this formulation proves to be a powerful alternative to other classic methods, considering the results presented.
KSCE Journal of Civil Engineering, 2020
Problems involving cavities or excavations are widely addressed in geomechanics, in both analytic... more Problems involving cavities or excavations are widely addressed in geomechanics, in both analytical and numerical approaches. The boundary element method (BEM) is well-known as an interesting choice for half plane problems, providing accurate results at a low computational cost. This work deals with the probabilistic analysis of circular tunnels embedded in elastic media, coupling a BEM formulation to a structural reliability model. The gravitational loading and material parameters are treated as random variables, whose statistical description is taken from the literature. The loadings considered include the vertical overburden stress and the lateral earth pressure. Regarding the reliability evaluation, first order reliability method (FORM) and Monte Carlo simulation technique are employed, being compared in terms of accuracy. Regarding the BEM model, the Multiple Reciprocity Method (MRM) is used in the evaluation of domain integrals, and the subregion technique is employed for the analysis of the tunnel lining. Some analyses are presented, in order to validate the coupled BEM-FORM model and apply it to the estimation of failure probability, evaluating the influence of the random variables taken into account in the probabilistic response. Structural reliability Boundary element method Half-plane problem Multiple reciprocity method FORM
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Papers by Philipe Almeida