Lattice domes reliability by the perturbation-based approaches vs. semi-analytical method

Abstract

Abstract An efficiency of the perturbation-based approaches in comparison with semi-analytical symbolic derivation of the probabilistic moments and coefficients has been verified in this work. Truncated equivalents for the classical linearized and iterative perturbation-based schemes have been created to enable considering of random variable probability density function upper and lower bounds in stochastic perturbation scheme. Higher order Taylor expansions have been used also in the derivation of probabilistic characteristics to analyze probabilistic convergence of the perturbation schemes for non-polynomial structural responses. These computations have been completed using the Finite Element Method on the example of the structural state variables of axisymmetric spherical steel skeletal dome structures. Four basic different types (ribbed, Schwedler, geodesic as well as diamatic) have been compared here in the context of time-independent reliability assessment in the presence of uncertainty in the structural steel Young modulus. Truncated iterative stochastic perturbation technique (TISPT) has turned out to be the most sufficient approach giving a global gain in the accuracy of the results with perturbation order increase, which is remarkably slower for higher probabilistic characteristics. The most appropriate results have been provided by using the same Taylor expansion of a given response function substituted into the subsequent probabilistic moments formulas.