Reduced basis technique for collapse analysis of shells
A hybrid finite-element Rayleigh-Ritz technique is used to predict the collapse behavior of shells. In this hybrid technique, the modeling versatility of the finite-element method is preserved, and a significant reduction in the number of degrees of freedom is achieved by expressing the nodal displacement vector as a linear combination of a small number of basis vectors. A Rayleigh-Ritz technique is used to approximate the finite-element equations of the discretized shell by a reduced system of nonlinear algebraic equations. A scalar function is introduced to measure the degree of nonlinearity of the structure for the case of loading applied by means of axial end shortening. Also, a quantitative measure for the error of the reduced system of equations is proposed. Some insight is given as to why and when the reduced basis technique works, and the effectiveness of the technique for predicting the collapse behavior of shells is demonstrated by means of a numerical example of elastic collapse of an axially compressed pear-shaped cylinder.