Stochastic analysis of highly non-linear structures

Abstract

SUMMARYInstabilities can introduce highly non-linear effects into structural problems. The instabilities, not clearly associated with a change in a parameter, result in a stochastic variation of the responses. This process variation can be distinguished from the effects of the parameter variation by mapping the response variation onto a predictable space and a residual space, where the predictable space contains the possible effects of the parameter variation, and the residual space contains the process effects. This study discusses the sources (mechanics) of the response variation in this class of problems, the use of response surfaces to distinguish between effects driven by design variable changes and bifurcations, and the visualization of unstable zones in the structure. Analytical problems, a headform impact problem, and an occupant safety study clarify the use of the proposed methodology.

Detection of branching points in noisy processes

“…This includes the membership values µ k,r from Eqs. (24) and (25) in the evaluation of the fuzzy cluster configurationC = {C k , k = 1, . .…”

“…c Process group C 3 (τ ). d Representative processes records p i (τ ) crashworthiness design of vehicle structures [25]. Significant effort is made to reveal the mechanical background for the branching of the time histories to identify characteristic failure modes.…”

“…This is a typical problem in crashworthiness investigations. Both experiments and numerical analyses are characterized by significant noise [9,20,25,27]. An example of a stochastic numerical crash analysis is shown in Fig.…”

Designing robust structures – A nonlinear simulation based approach

“…Beyond civil engineering, endeavor in probabilistic robust design is made, in particular, in vehicle and aerospace industry. Those developments are primarily focused on economic and effective exploitation of material properties [12], on the safety of passengers [22,23], and on improvements in cost and quality management.…”

Design and analysis for the Gaussian process model

“…Examples of applications of the maximin designs can be found in Jank and Shmueli 23 , Liefvendahl and Stocki 24 , Chen et al 25 , Roux et al 26 , and Bursztyn and Steinberg 27 . Sphere packing designs are impressive at filling space, but their drawback is that they do not maintain uniform spacing when projecting into a lower-dimensional space.…”