TABLE OF CONTENTS People are divided into two categories: from one side those who see the variational formulation of a physical law the apotheosis of economy of nature; from the other side those who deny them any interest and affirm that they can be formulated only after the physical law of the phenomenon is established E. Tonti (1969).
It is clear that for any probabilistic modeling of a physical system to be useful, it has to be compatible with the available numerical schemes R. G. Ghanem and P. D. Spanos (1991c).
A variational formulation of a theory for physical processes has several advantages the variational formulation provides a sound basis for an approximate formulation of the problem. Theories of beams, plates and shells, but also finite element models are typical examples of such approximate formulation J. F. Besseling (1985).
We cannot take anything for granted, beyond the first mathematical formula. Question everything else M. Mitchell.
variational or weak forms of the laws of mechanics are often considered to be the only natural and rigorously correct way to think about them M. Kleiber and T. D. Hien (1993).
For the beam bending problems considered in the previous chapter, both the spatially random material parameter (Young's modulus) and the geometrical parameters (dimension of the cross-section) were combined into one parameter (the bending stiffness). The governing equation for beam bending, constituting a differential equation with a spatially varying random coefficient, along with random boundary conditions, was derived. The solution for the mean and covariance...
