Claudio Roberto Ávila da Silva Junior | Universidade Tecnológica Federal do Paraná - campus Curitiba - Brazil

• Grant number: 08/10366-4
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Duration: March 06, 2009 - June 05, 2009
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: André Teófilo Beck
• Grantee: André Teófilo Beck
• Visiting researcher: Claudio Roberto Avila da Silva Junior
• Visiting researcher institution: Universidade Tecnológica Federal do Paraná (UTFPR). Campus Curitiba, Brazil
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The department of Structural Engineering of the São Carlos School of Engineering, University of São Paulo, has a tradition of many years in the development of numerical techniques for solution of structural analysis problems. Such techniques include the finite element method, meshless methods and boundary element methods. Just recently, the department received important incentive to continue this research line, by means of FAPESP's support to the thematic project entitled "Development of numerical Methods for Structural Analysis" - process number 2006/50594-0 - under coordination of Prof. Wilson Sérgio Venturini [8].In this research line, there has always been attention to the representation and treatment of uncertainties inherent to structural engineering problems, in what can be called a probabilistic approach. This approach is evidenced in a number research studies developed in the department, in particular by Prof. Venturini, and mode recently by André Beck [references 1 to 7]. One particularity of the developed studies is the separation between the mechanical and probabilistic parts of the problem, by use of structural reliability methods. This separation allows deterministic finite element programs to be used to solve the mechanical part of the problem, whereas an independent reliability program solves the probabilistic part of the problem. This technique was used to develop a structural reliability program, which has been extensively used in the department: "Computational Program for Reliability Analysis of Structures" - process FAPESP 2006/00154-4 [9].With the visit of Prof. Claudio Avila, we would like to nucleate a new research line at the department, within the probabilistic approach to structural engineering problems. In the so called "Stochastic Finite Element Method", the treatment of uncertainty is not done at the level of computational solution of the problem, but at the formulation level. This means that uncertainty is incorporated in the governing differential equation of the problem, and a solution is constructed for the resulting stochastic differential equation. Clearly, this means that deterministic finite element programs cannot be used: stochastic finite element programs have to be developed to handle different types of structural engineering problems. The stochastic finite element line of research is actually in ample development, in international level, as can be verified by publication in the main journals of the area. Prof. Avila has been dedicating himself to this subject since starting his doctoral program in 2001. Follows a description of the subject by Prof. Avila.This research project proposes the study and computational implementation of methods for the analysis of stochastic structural engineering problems. Problems of plane elasticity and bending of Kirchhoff and Mindlin plates will be addressed. Uncertainty will be admitted in the material properties, and modeled by random variables or stochastic processes. The Galerkin finite element method will be employed. The approximation space will be constructed by chaos polynomials, originating from the Askey-Wiener scheme. Monte Carlo simulation will be used to evaluate the approximated solutions obtained via Galerkin method. A computational package to solve stochastic structural problems, of academic purposes, will be developed. This package shall include algorithms for mesh generation, solution of linear and non-linear systems of equations, solution of generalized eigenvalue problems, mathematical programming and sensitivity analysis. In order to facilitate maintenance and future developments, object oriented programming techniques will be employed. (AU)

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BECK, ANDRE TEOFILO; DA SILVA, JR., CLAUDIO R. A.. Timoshenko versus Euler beam theory: Pitfalls of a deterministic approach. STRUCTURAL SAFETY, v. 33, n. 1, p. 19-25, 2011. (08/10366-4)

SILVA, C. R. A.; AZIKRI DE HEUSI, H. P.; MANTOVANI, G. E.; BECK, A. T.. Galerkin Solution of Stochastic Beam Bending on Winkler Foundations. CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, v. 67, n. 2, p. 119-149, OCT 2010. (08/10366-4)

AVILA DA SILVA, JR., C. R.; BECK, ANDRE TEOFILO; FRANCO, ADMILSON T.; DE SUAREZ, OSCAR A.. Galerkin Solution of Stochastic Reaction-Diffusion Problems. JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME, v. 135, n. 7, JUL 2013. (08/10366-4)

AVILA DA SILVA, JR., CLAUDIO R.; BECK, ANDRE TEOFILO. Chaos-Galerkin solution of stochastic Timoshenko bending problems. COMPUTERS & STRUCTURES, v. 89, n. 7-8, p. 599-611, APR 2011. (08/10366-4)

DA SILVA, JR., CLAUDIO R. AVILA; BECK, ANDRE TEOFILO. Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme. PROBABILISTIC ENGINEERING MECHANICS, v. 25, n. 2, p. 172-182, APR 2010. (08/10366-4)