A. Colombo¹, U. Galvanetto²

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.3, pp. 235-254, 2009, DOI:10.3970/cmes.2009.053.235

Abstract The paper addresses the problem of computing the stable manifolds of equilibria and limit cycles of saddle type in piecewise smooth dynamical systems. All singular points that are generically present along one-dimensional or two-dimensional manifolds are classified and such a classification is then used to define a method for the numerical computation of the stable manifolds. Finally the proposed method is applied to the case of a stick-slip oscillator. More >

Chein-Shan Liu ^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 73-94, 2007, DOI:10.3970/cmes.2007.017.073

Abstract The primary objectives of the present exposition focus on five different types of representations of the plastic equations obtained from an elastic-perfectly plastic model by employing different corotational stress rates. They are (a) an affine nonlinear system with a finite-dimensional Lie algebra, (b) a canonical linear system in the Minkowski space, (c) a non-canonical linear system in the Minkowski space, (d) the Lie-Poisson bracket formulation, and (e) a two-generator and two-bracket formulation. For the affine nonlinear system we prove that the Lie algebra of the vector fields is so(5,1), which has dimensions fifteen, and by the… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 161-180, 2006, DOI:10.3970/cmes.2006.012.161

Abstract Materials' internal spacetime may bear certain similarities with the external spacetime of special relativity theory. Previously, it is shown that material hardening and anisotropy may cause the internal spacetime curved. In this paper we announce the third mechanism of mixed-control to cause the curvedness of internal spacetime. To tackle the mixed-control problem for a Prager kinematic hardening material, we demonstrate two new formulations. By using two-integrating factors idea we can derive two Lie type systems in the product space of M^m+1⊗Mⁿ⁺¹. The Lie algebra is a direct sum of so(m,1)⊕so(n,1), and correspondingly the symmetry group is… More >