SOLID SIMULATION

Solid Simulation

Abstract

The main purpose of this paper is two-fold: first, to present a critical review of available errorcontrolled adaptive finite element methods—with absolute global and goal-oriented error estimates— for approximate solutions of a given mathematical model and the model error of the mathematical model considered and its dimensions, enhanced with our own recent results in fracture mechanics. The second related important matter is which physical/mathematical models—including various boundary layers and other disturbances—and which accuracy of the finite element solutions in which norm are prescribed and necessary for the safety and reliability of a certain engineering problem, e.g. in structural engineering, of course depending on materials, systems and the type as well as the magnitude of prescribed loadings (i.e. actions in a factorized concept) acting on a specific structure. It can be observed that behind the existing codes there still lies the old thinking of, e.g., classical elastic beam theory of so-called second order for stability problems and the corresponding elastic potential for plates and shells in buckling. Modern flexible finite element modelling by deriving theories in variational form for thin-walled beams, plates and shells from rather general 3D theories, for both linear and non-linear problems, capturing inelastic deformations and layer effects by material and dimensional expansions are not addressed in the Eurocodes for structural engineering. The necessary consequence is that joint work of computational mechanics specialists and structural engineers, working in national and international code committees, is absolutely necessary, in order to avoid a lot of costly troubles and dangers of today by improving and updating the existing codes.

Table of Content

Abstract2

Introduction4

Extent of Model4

Type of Symmetry5

Restraints and Loading6

Approx. Stress Calculation7

Approx. displacement calculation7

Finite Element Model7

Restraints Applied as Intended10

Load as Intended11

Mash Grading Explained and Demonstrated12

Discussion of Results12

Convergence Displacement - Error Estimated13

Convergence Stress - Error Estimated15

References16

Solid Simulation

Introduction

The goal of reliable and efficient engineering analysis is the proof of material and structural resistance against all possible loadings (actions) with sufficient safety at minimal cost, guaranteeing full usability within lifetime. Codes, standards and technical rules sufficiently support the engineering design of most technical components in all engineering fields. But requirements and instructions for adequate mechanical modelling and the prescribed accuracy of static and dynamic analysis are not included. The thinking behind these codes is obviously still influenced by classical beam and plate models for which 'exact' analytical or numerical solutions by series are possible under a couple of restricting conditions, but not by the concepts of todays computational mechanics where modelling can be done much closer to structural and system reality but, of course, the approximation errors have to be considered (Babuska, 2007, 40).

Extent of Model

In this context it should be mentioned that approximated point supports and single forces of beams cannot be transferred to plates in plain stress or bending states because of the artificially generated singularities. One has to realise that smooth solutions of beams with fourth-order differential equations are in H4-function spaces, whereas corresponding smooth solutions of plates with second-order partial differential equations are only in ...