Strict upper and lower bounds of quantities for beams on elastic foundation by dual analysis

Abstract

2015),"Consistent crystal plasticity kinematics and linearization for the implicit finite element method", Engineering Computations, Vol. 32 Iss 6 pp. 1526-1548 http://dx.If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. AbstractPurpose -The purpose of this paper is to acquire strict upper and lower bounds on quantities of slender beams on Winkler foundation in finite element analysis. Design/methodology/approach -It leans on the dual analysis wherein the constitutive relation error (CRE) is used to perform goal-oriented error estimation. Due to the coupling of the displacement field and the stress field in the equilibrium equations of the beam, the prolongation condition for the stress field which is the key ingredient of CRE estimation is not directly applicable. To circumvent this difficulty, an approximate problem and the solution thereof are introduced, enabling the CRE estimation to proceed. It is shown that the strict bounding property for CRE estimation is preserved and strict bounds of quantities of the beam are obtainable thereafter. Findings -Numerical examples are presented to validate the strict upper and lower bounds for quantities of beams on elastic foundation by dual analysis. Research limitations/implications -This paper deals with one-dimensional (1D) beams on Winkler foundation. Nevertheless, the present work can be naturally extended to analysis of shells and 2D and 3D reaction-diffusion problems for future research. Originality/value -CRE estimation is extended to analysis of beams on elastic foundation by a decoupling strategy; strict upper bounds of global energy norm error for beams on elastic foundation are obtained; strict bounds of quantities for beams on elastic foundation are also obtained; unified representation and corresponding dual analysis of various quantities of the beam are presented; rigorous derivation of admissible stresses for beams is given.

Strict upper and lower bounds for quantities of interest in static response sensitivity analysis

“…and they can be constructed based on {u h , U h } using the recovery technique proposed in [37]. Employing the inverse transformation of (74), { M res h , μres h } are obtained as…”

“…Among the available techniques, the CRE-based error estimation provides guaranteed strict bounds of quantities. The strict bounding property, together with its advantage of wide applicability [28][29][30][31][32][33][34][35][36][37][38], makes the CRE stand out for goal-oriented error estimation.…”