New B-Spline Finite Element approach for geometrical design and mechanical analysis

Abstract

In most existing CAD systems, geometrical design and mechanical analysis are operated as completely separate modules. Intensive interaction between these modules is, however, highly desired due to the iterative nature of a typical product development process. Formulating a new, unified approach to design and analysis that provides a high level of interaction is the main purpose of this research. The idea is to integrate a mechanically based geometrical design concept with the mechanical analysis module in a uniform B-Spline Finite Element (BSFE) environment. In this paper, the BSFE method is formulated and its validity and adequacy are verified for elastic linear rod and plate models. In particular, the feasibility of applying B-spline functions as base functions of the finite element method for design and analysis is demonstrated. Unique scheme attributes based on intrinsic properties of B-spline functions are investigated in detail. Method adequacy is demonstrated by comparing convergence characteristics, complexity and computational cost to the spectral element method.

Adaptive mesh generation based on multi-resolution quadtree representation

“…The method described in this paper is part of a comprehensive system for solving problems using FE and displaying them with post-processing. In the future, this method will be integrated with the BSFE system that was developed [16].…”

NURBS‐enhanced finite element method (NEFEM)

“…Moreover, classical polynomial approximations of the solution are abandoned and the solution is approximated with the same basis used in the CAD environment. The first application is again encountered on shape optimization, using B-Splines for the geometrical description and for the mechanical analysis, see [53]. In the 2000s, more advanced CAD technology have been applied following the same rationale.…”

IGA: A Simplified Introduction and Implementation Details for Finite Element Users

“…Kagan et al [7] introduced a B-spline based FE approach that combines the geometrical design and the analysis systems into a common framework. Later, based on the subdivision of surface scheme Cirak et al [8] presented a different paradigm for describing and modelling of the thin shells geometries in the FEA framework.…”