SOLUTION OF THE STOCHASTIC BEAM BENDING PROBLEM BY GALERKIN METHOD AND THE ASKEY-WIENER SCHEME

Authors

  • CLÁUDIO ROBERTO ÁVILA DA SILVA JR.
  • ANDRÉ T. BECK
  • EDISON DA ROSA

Abstract

IN THIS PAPER, THE ASKEY-WIENER SCHEME AND THE GALERKIN METHOD ARE USED TO OBTAIN APPROXIMATE SOLUTIONS TO THE STOCHASTIC BEAM BENDING PROBLEM. THE STUDY ADDRESSES EULER-BERNOULLI BEAMS WITH UNCERTAIN BENDING STIFFNESS MODULUS. THE UNCERTAINTY IS REPRESENTED AS A PARAMETERIZED STOCHASTIC PROCESS. THE SPACE OF APPROXIMATE SOLUTIONS IS BUILT USING RESULTS OF DENSITY BETWEEN THE SPACE OF CONTINUOUS FUNCTIONS AND SOBOLEV SPACES. FROM THE APPROXIMATE SOLUTION, FIRST AND SECOND ORDER MOMENTS OF THE RESPONSE ARE DERIVED, AND COMPARED WITH THE CORRESPONDING ESTIMATES OBTAINED VIA MONTE CARLO SIMULATION. RESULTS SHOW VERY FAST CONVERGENCE TO THE EXACT SOLUTION, AT EXCELLENT ACCURACIES.

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Published

2009-03-01

Issue

Vol. 6 No. 1 (2009)

Section

Articles

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