Uncertainty quantification based on pillars of experiment, theory, and computation. Part II: Theory and computation

•This paper deals with theoretical and computational aspects of different uncertainty calculi, introduced in Part I, specifically when the data is bounded by either of the following five figures: triangle, rectangle, parallelogram, ellipse or super ellipse.•Comparison is conducted between the treated uncertainty calculi with preference given to the one which predicts the least estimate for the favorable response.

This paper deals with theoretical and computational aspects of different uncertainty calculi, introduced in Part I, specifically when the data is bounded by any of the following five figures: triangle; rectangle; parallelogram; ellipse or super ellipse. We consider elastic structures subjected to uncertainty, and evaluate the least favorable, maximum response and the most favorable, minimum response. Comparison is conducted between the treated uncertainty calculi with preference given to the one which predicts the least estimate for the favorable response. In considered elastic structures the solution or displacements is available analytically; in cases when analytical solution is absent purely numerical solution ought to be implemented. Such a case is now under development and will be published elsewhere.