Theory of GJ-integral and its application for shape optimization
Dept. of Information Design, Hiroshima Kokusai Gakuin University, Hiroshima, Japan
GJ-integral came from J-integral in the 2-dimensional fracture mechanics, and is proposed by the author to express quantity of 3-dimensional crack extension. Later, the concept of GJ-integral has been developed to express the variation of potential energies with respect to singularities, that is, boundaries, the interface between the parts with different boundary conditions and cracks. In this talk, I will show the application of GJ-integral to shape optimization, using two different cost functional, namely total potential energy and the integral of the function of solution over the domain. The method is applicable to the weak solution of partial differential equation/system that may not be the strong solution and also to non-linear problem when the cost functional is total potential energy.