Ph.D Thesis

Ph.D StudentKagan Pavel
SubjectNew B-spline Finite Element Approach for Integrated
Mechanically Based Design and Analysis
DepartmentDepartment of Mechanical Engineering
Supervisors PROF. Anath Fischer


In current computer aided engineering (CAE) systems, each iteration between geometric design and mechanical analysis requires remodeling the object and converting its mathematical representation. In this work, a new concept for an integrated mechanically based CAE system was developed to overcome these problems. The proposed system consists of the computer aided geometric design (CAGD) module and the mechanical analysis module. The proposed CAGD module implements the mechanically based geometric design concept. Consequently, both modules are based on mechanical models of the design object and employ the same B-spline finite element (BSFE) computational environment and the same mathematical B-spline representation.

In this work, the elastic linear Kirchhoff plate model was used for creating sculptured surfaces, while the elastic linear solid model was used for creating sculptured volumetric solid objects. Although the proposed approach is not restricted to elastic linear models, they were chosen since they provide a highly intuitive shape response to applied forces and geometric constraints.

Within the scope of surface sculpting, two B-spline finite elements were used for analyzing the Kirchhoff plate model. These are the quadrilateral mixed plate BSFE for creating approximate smooth surfaces, and the C1 conforming quadrilateral Hermite BSFE for creating exact smooth surfaces.

Two methods were developed and implemented for adaptive refinement of a BSFE solution within the proposed CAE system. These are a local variant of np-refinement and a local variant of h-refinement. In the scope of developing sculptured surfaces, the proposed approach supports C0 as well as C1 continuous shapes. For sculptured solids, only C0 continuity has been considered so far.