Computational Engineering Development and Implementation of Computational Methods for Structural Analysis and Design
Doctoral thesis, 2001
'Computational engineering' (CE) is computation based on mathematical models for use in engineering design. CE can be used to study and optimise structures and processes in industry and other branches of society to utilise resources in the most effective way. Modelling, simulation, optimisation and visualisation are basic methods of CE. The current development of CE is concerned with increased realism, improved efficiency, reliability and quality control, and integration of methods to solve more complex problems. The purpose of this thesis is to contribute to the development of the field of CE. As a respond, the thesis attempts to give both an overview and detailed knowledge of computational methods. The examples are limited to structural engineering, but the methodology should have a wider range of application.
The thesis consists of five appended papers (A-E) and a summary. Paper A implements and tests mesh adaptive FE-analysis applied to plate bending problems. Paper B integrates CAD, FEM and optimisation programs in a nested loop for optimisation of a bridge structure. Paper C implements and tests the FEM90 program together with a CAD program in modelling and simulation of a major bridge structure. Paper D investigates methods to solve systems of non-linear equations as arising in FE-simulation of structures loaded to failure. Paper E implements and tests new pre-conditioned, iterative methods to solve large, multi-connected 3D problems. The summary gives an overview of the CE methods, and discusses computer implementation and integration of methods with the object-oriented FEM90 program as example.
Paper A confirms that the SPR(D) technique provides good error estimates and that re-meshing adaptivity is applicable also for plate bending problems. The optimisation in Paper B indicated substantial cost reductions for a common type of highway bridge. However, the nested program set-up was not ideal. Paper C showed that CAD and FEM could handle complex engineering structures. However, increased realism of the simulations required improvement of methods for solution of non-linear equations. Paper D indicated that a combination of dynamics and a trust region method might improve the solution of non-linear equations. Paper E showed that the multi-grid method with mesh adaptation extends the range of the FEM to large 3D problems.
The thesis shows that CE today consists of a number of useful but independent methods/programs. The object-oriented methodology provides a means to integrate the methods around data contained in natural objects defined by classes. The presentation proposes the development of generally applicable classes for use in the solution of realistic engineering problems.