BOUNDS ANALYSIS OF A BEAM BASED ON THE CONVEX MODEL OF UNCERTAIN FOUNDATION

✍ Scribed by L. Fryba; N. Yoshikawa

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 214 KB
• Volume: 212
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1997.1482

✦ Synopsis

A methodology of bounds analysis based on the convex set of uncertainty is presented. An infinitely long beam on an uncertain foundation is subjected to a moving force with constant speed. The steady state vibration is analysed in the context of the finite element method. Uncertainty variables representing the uncertain fluctuation of foundation stiffness is confined within a convex hull given as a hyperellipse. The fluctuation of dynamic responses of the beam, that is, the vertical deflection and the bending moment are approximated to a first-order with respect to the uncertainty variables. The upper and lower bounds of the response fluctuations are identified on the boundary of the convex model by means of the Lagrange multiplier method. Numerical analysis demonstrates the validity of the proposed formulation for various constant speeds of the moving force. The analysis is summarized in terms of the worst response, which is the maximum absolute value of the response within the identified bounds.