jNURBS: An object-oriented, symbolic framework for integrated, meshless analysis and optimal design

In this paper, we propose a design-analysis integrated CAD framework termed jNURBS. jNURBS, developed using the Java language, is an extensible, Object-Oriented framework that enables meshless analysis of physical behavior and optimal design. The geometry as well as the analysis fields (displacement, temperature, etc.) are described mathematically using a common representation, namely the Non-Uniform Rational B-Spline (NURBS). Thus, NURBS serves to design the geometry as well as carryout meshless analysis thereby integrating the design and analysis in an efficient manner. The program kernel provides tools to symbolically describe complex multi-physics problems, methods to manipulate the NURBS entities, a set of primitive NURBS entities, and an iterative optimization solver. The problems are symbolically defined using a newly developed high-level, natural language description through an interface termed JNS (jNURBS Script). A number of example problems, selected from meshless structural analysis, material microstructure simulation, shape optimal design, and equilibrium shape of droplets, are presented to demonstrate the effectiveness and versatility of the framework.