An isogeometric Reissner-Mindlin shell derived from the continuum theory is presented. The geometry is described by NURBS surfaces. The kinematic description of the employed shell theory requires the interpolation of the director vector and of a local basis system. Hence, the definition of nodal basis systems at the control points is necessary for the proposed formulation. The control points are in general not located on the shell reference surface and thus, several choices for the nodal values are possible. The proposed new method uses the higher continuity of the geometrical description to calculate nodal basis system and director vectors which lead to geometrical exact interpolated values thereof. Thus, the initial director vector coincides with the normal vector even for the coarsest mesh. In addition to that a more accurate interpolation of the current director and its variation is proposed. Instead of the interpolation of nodal director vectors the new approach interpolates nodal rotations. Account is taken for the discrepancy between interpolated basis systems and the individual nodal basis systems with an additional transformation. The exact evaluation of the initial director vector along with the interpolation of the nodal rotations lead to a shell formulation which yields precise results even for coarse meshes. The convergence behavior is shown to be correct for k-refinement allowing the use of coarse meshes with high orders of NURBS basis functions. This is potentially advantageous for applications with high numerical effort per integration point. The geometrically nonlinear formulation accounts for large rotations. The consistent tangent matrix is derived. Various standard benchmark examples show the superior accuracy of the presented shell formulation. A new benchmark designed to test the convergence behavior for free form surfaces is presented. Despite the higher numerical effort per integration point the improved accuracy yields considerable savings in computation cost for a predefined error bound.

In this contribution, a mortar-type method for the coupling of non-conforming NURBS (Non-Uniform Rational B-spline) surface patches is proposed. The connection of non-conforming patches with shared degrees of freedom requires mutual refinement, which propagates throughout the whole patch due to the tensor-product structure of NURBS surfaces. Thus, methods to handle non-conforming meshes are essential in NURBSbased isogeometric analysis. The main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation. The deformations of the interface control points of adjacent patches are interrelated with a master-slave relation. This relation is established numerically using the weak form of the equality of mutual deformations along the interface. With the help of this relation, the interface degrees of freedom of the slave patch can be condensated out of the system. A natural connection of the patches is attained without additional terms in the weak form. The proposed method is also applicable for nonlinear computations without further measures. Linear and geometrical nonlinear examples show the high accuracy and robustness of the new method. A comparison to reference results and to computations with the Lagrange multiplier method is given.The combination of these two issues requires methods to handle non-conforming patches in order to establish an efficient mechanical response analysis framework for the computation of complex NURBS surface models.Domain decomposition methods decompose the domain of a given problem into subdomains, of which the parametrization does not have to match. The situation at hand is an ideal field of application for domain decomposition methods, where each patch can be regarded as one subdomain. A general overview over domain decomposition methods is given in [6]. The Penalty method [7], the Lagrange multiplier method [8], and Nitsche's method [9] were proposed in the 1970s to enforce Dirichlet boundary conditions in a weak manner. In recent engineering literature, these methods are used as a basis for domain decomposition techniques. Mortar methods are the prevailing domain decomposition method in mathematical literature. Basically, two standard types of mortar formulations exist, which are referred to as the non-conforming positive definite problem and the saddle point problem based on unconstrained product spaces in [6]. In all cases, a Lagrange multiplier space is used for the matching conditions along the interface. The mortar method leading to the nonconforming positive definite problem was initially proposed by Bernardi et al. [10]. The function spaces are constrained to fulfill the matching condition at the interface in a weak manner. Basically, this means that the basis functions of one side are related to those of the other side in a way that the matching condition is fulfilled. The discretization of the interface condition with Lagrange multiplier functions yields an equation...

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