The focus of the current contribution is on the development of the unified geometrical formulation of contact algorithms in a covariant form for various geometrical situations of contacting bodies leading to contact p...The focus of the current contribution is on the development of the unified geometrical formulation of contact algorithms in a covariant form for various geometrical situations of contacting bodies leading to contact pairs: surface-to-surface, line-to-surface, point-to-surface, line-to-line, point-to-line, point-to-point. The construction of the corresponding computational contact algorithms are considered in accordance with the geometry of contact bodies in a covariant form. These forms can be easily discredited within finite element methods independently of order of approximation and, therefore, the result is straightforwardly applied within iso-geometric finite element methods. This approach is recently became known as geometrically exact theory of contact interaction [10]. Application for contact between bodies with iso- and anisotropic surface, for contact between cables and curvilinear beams as well as recent development for contact between cables and bodies is straightforward. Recent developments include the improvement of the curve-to-surface (deformable) contact algorithm.展开更多
Many works have investigated the problem of reparameterizing rational B^zier curves or surfaces via MSbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weig...Many works have investigated the problem of reparameterizing rational B^zier curves or surfaces via MSbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weights becomes smallerthat some algebraic and computational properties of the curves or surfaces can be improved in a way. However, it is an indication of veracity and optimization of the reparameterization to do prior to judge whether the maximal ratio of weights reaches minimum, and verify the new weights after MSbius transfor- mation. What＇s more the users of computer aided design softwares may require some guidelines for designing rational B6zier curves or surfaces with the smallest ratio of weights. In this paper we present the necessary and sufficient conditions that the maximal ratio of weights of the curves or surfaces reaches minimum and also describe it by using weights succinctly and straightway. The weights being satisfied these conditions are called being in the stable state. Applying such conditions, any giving rational B6zier curve or surface can automatically be adjusted to come into the stable state by CAD system, that is, the curve or surface possesses its optimal para- metric distribution. Finally, we give some numerical examples for demonstrating our results in important applications of judging the stable state of weights of the curves or surfaces and designing rational B6zier surfaces with compact derivative bounds.展开更多
This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precisio...This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precision and the shape of the interpolation surface. An approach to determining the freedom degrees is given, the continuity equations for constructing C2 quartic spline curve are discussed, and a new method for constructing C2 quartic spline surface is presented. The advantages of the new method are that the equations that the surface has to satisfy are strictly row diagonally dominant, and the discontinuous points of the surface are at the given data points. The constructed surface has the precision of quartic polynomial. The comparison of the interpolation precision of the new method with cubic and quartic spline methods is included.展开更多
文摘The focus of the current contribution is on the development of the unified geometrical formulation of contact algorithms in a covariant form for various geometrical situations of contacting bodies leading to contact pairs: surface-to-surface, line-to-surface, point-to-surface, line-to-line, point-to-line, point-to-point. The construction of the corresponding computational contact algorithms are considered in accordance with the geometry of contact bodies in a covariant form. These forms can be easily discredited within finite element methods independently of order of approximation and, therefore, the result is straightforwardly applied within iso-geometric finite element methods. This approach is recently became known as geometrically exact theory of contact interaction [10]. Application for contact between bodies with iso- and anisotropic surface, for contact between cables and curvilinear beams as well as recent development for contact between cables and bodies is straightforward. Recent developments include the improvement of the curve-to-surface (deformable) contact algorithm.
基金Supported by the National Nature Science Foundations of China(61070065)
文摘Many works have investigated the problem of reparameterizing rational B^zier curves or surfaces via MSbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weights becomes smallerthat some algebraic and computational properties of the curves or surfaces can be improved in a way. However, it is an indication of veracity and optimization of the reparameterization to do prior to judge whether the maximal ratio of weights reaches minimum, and verify the new weights after MSbius transfor- mation. What＇s more the users of computer aided design softwares may require some guidelines for designing rational B6zier curves or surfaces with the smallest ratio of weights. In this paper we present the necessary and sufficient conditions that the maximal ratio of weights of the curves or surfaces reaches minimum and also describe it by using weights succinctly and straightway. The weights being satisfied these conditions are called being in the stable state. Applying such conditions, any giving rational B6zier curve or surface can automatically be adjusted to come into the stable state by CAD system, that is, the curve or surface possesses its optimal para- metric distribution. Finally, we give some numerical examples for demonstrating our results in important applications of judging the stable state of weights of the curves or surfaces and designing rational B6zier surfaces with compact derivative bounds.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 60173052)Shandong Province Key Natural Science Foundation (Grant No. Z2001G01).
文摘This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precision and the shape of the interpolation surface. An approach to determining the freedom degrees is given, the continuity equations for constructing C2 quartic spline curve are discussed, and a new method for constructing C2 quartic spline surface is presented. The advantages of the new method are that the equations that the surface has to satisfy are strictly row diagonally dominant, and the discontinuous points of the surface are at the given data points. The constructed surface has the precision of quartic polynomial. The comparison of the interpolation precision of the new method with cubic and quartic spline methods is included.
