Realization of CAD-integrated shell simulation based on isogeometric B-Rep analysis

An entire design-through-analysis workflow solution for isogeometric B-Rep analysis (IBRA), including both the interface to existing CADs and the analysis procedure, is presented. Possible approaches are elaborated for the full scope of structural analysis solvers ranging from low to high isogeometric simulation fidelity. This is based on a systematic investigation of solver designs suitable for IBRA. A theoretically ideal IBRA solver has all CAD capabilities and information accessible at any point, however, realistic scenarios typically do not allow this level of information. Even a classical FE solver can be included in the CAD-integrated workflow, which is achieved by a newly proposed meshless approach. This simple solution eases the implementation of the solver backend. The interface to the CAD is modularized by defining a database, which provides IO capabilities on the base of a standardized data exchange format. Such database is designed to store not only geometrical quantities but also all the numerical information needed to realize the computations. This feature allows its use also in codes which do not provide full isogeometric geometrical handling capabilities. The rough geometry information for computation is enhanced with the boundary topology information which implies trimming and coupling of NURBS-based entities. This direct use of multi-patch trimmed CAD geometries follows the principle of embedding objects into a background parametrization. Consequently, redefinition and meshing of geometry is avoided. Several examples from illustrative cases to industrial problems are provided to demonstrate the application of the proposed approach and to explain in detail the proposed exchange formats.

[1]  Tod A. Laursen,et al.  A Nitsche embedded mesh method , 2012 .

[2]  Zheng-Dong Ma,et al.  Nonconforming isogeometric analysis for trimmed CAD geometries using finite-element tearing and interconnecting algorithm , 2017 .

[3]  Roland Wüchner,et al.  Integrated design and analysis of structural membranes using the Isogeometric B-Rep Analysis , 2016 .

[4]  Nicholas S. North,et al.  T-spline simplification and local refinement , 2004, SIGGRAPH 2004.

[5]  R. Echter,et al.  A hierarchic family of isogeometric shell finite elements , 2013 .

[6]  Hung Nguyen-Xuan,et al.  Explicit finite deformation analysis of isogeometric membranes , 2014 .

[7]  Ernst Rank,et al.  Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries , 2014 .

[8]  Ekkehard Ramm,et al.  A shear deformable, rotation-free isogeometric shell formulation , 2016 .

[9]  Roland Wüchner,et al.  Embedded structural entities in NURBS-based isogeometric analysis , 2017 .

[10]  Peter Hansbo,et al.  CutFEM: Discretizing geometry and partial differential equations , 2015 .

[11]  Les A. Piegl,et al.  The NURBS book (2nd ed.) , 1997 .

[12]  Thomas-Peter Fries,et al.  Stable Isogeometric Analysis of Trimmed Geometries , 2016, ArXiv.

[13]  F. Brezzi,et al.  A discourse on the stability conditions for mixed finite element formulations , 1990 .

[14]  B. Simeon,et al.  Isogeometric Reissner–Mindlin shell analysis with exactly calculated director vectors , 2013 .

[15]  Pooyan Dadvand,et al.  A framework for developing finite element codes for multi-disciplinary applications. , 2007 .

[16]  Thomas J. R. Hughes,et al.  Blended isogeometric shells , 2013 .

[17]  Michael Griebel,et al.  A Particle-Partition of Unity Method Part V: Boundary Conditions , 2003 .

[18]  Barbara Wohlmuth,et al.  Isogeometric mortar methods , 2014, 1407.8313.

[19]  Yujie Guo,et al.  Weak Dirichlet boundary conditions for trimmed thin isogeometric shells , 2015, Comput. Math. Appl..

[20]  Tod A. Laursen,et al.  On methods for stabilizing constraints over enriched interfaces in elasticity , 2009 .

[21]  Y. Bazilevs,et al.  Weakly enforced essential boundary conditions for NURBS‐embedded and trimmed NURBS geometries on the basis of the finite cell method , 2013 .

[22]  Gábor Renner,et al.  Exact and approximate computation of B-spline curves on surfaces , 2004, Comput. Aided Des..

[23]  David J. Benson,et al.  On the numerical integration of trimmed isogeometric elements , 2015 .

[24]  Roland Wüchner,et al.  Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures , 2015 .

[25]  Ernst Rank,et al.  The finite cell method for three-dimensional problems of solid mechanics , 2008 .

[26]  Isaac Harari,et al.  A robust Nitsche's formulation for interface problems with spline‐based finite elements , 2015 .

[27]  Roland Wüchner,et al.  Nonlinear isogeometric spatial Bernoulli Beam , 2016 .

[28]  Dominik Schillinger,et al.  A parameter-free variational coupling approach for trimmed isogeometric thin shells , 2017 .

[29]  B. Wohlmuth,et al.  A comparison of mortar and Nitsche techniques for linear elasticity , 2004 .

[30]  Peter Wriggers,et al.  A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method , 2012 .

[31]  W. Dornisch,et al.  An efficient and robust rotational formulation for isogeometric Reissner–Mindlin shell elements , 2016 .

[32]  John A. Evans,et al.  Isogeometric analysis using T-splines , 2010 .

[33]  J. Dolbow,et al.  Imposing Dirichlet boundary conditions with Nitsche's method and spline‐based finite elements , 2010 .

[34]  Thomas J. R. Hughes,et al.  A large deformation, rotation-free, isogeometric shell , 2011 .

[35]  C. D. Boor,et al.  On Calculating B-splines , 1972 .

[36]  Benjamin Marussig,et al.  A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects , 2017, Archives of Computational Methods in Engineering.

[37]  Ralf Müller,et al.  Dual and approximate dual basis functions for B-splines and NURBS – Comparison and application for an efficient coupling of patches with the isogeometric mortar method , 2017 .

[38]  Josef Kiendl,et al.  Isogeometric Analysis and Shape Optimal Design of Shell Structures , 2011 .

[39]  Thomas J. R. Hughes,et al.  Isogeometric shell analysis: The Reissner-Mindlin shell , 2010 .

[40]  L. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communications.

[41]  Wayne Tiller,et al.  Geometry-based triangulation of trimmed NURBS surfaces , 1998, Comput. Aided Des..

[42]  Y. Bazilevs,et al.  Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method , 2012 .

[43]  Onur Atak,et al.  A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces , 2017 .

[44]  Thomas J. R. Hughes,et al.  Variationally consistent isogeometric analysis of trimmed thin shells at finite deformations, based on the STEP exchange format , 2018, Computer Methods in Applied Mechanics and Engineering.

[45]  C. D. Boor,et al.  On Calculating with B-Splines II. Integration , 1976 .

[46]  Martin Ruess,et al.  Nitsche’s method for a coupling of isogeometric thin shells and blended shell structures , 2015 .

[47]  Roland Wüchner,et al.  Isogeometric analysis of trimmed NURBS geometries , 2012 .

[48]  Ekkehard Ramm,et al.  A General Finite Element Approach to the form Finding of Tensile Structures by the Updated Reference Strategy , 1999 .

[49]  Roland Wüchner,et al.  Domain Decomposition Methods and Kirchhoff-Love Shell Multipatch Coupling in Isogeometric Analysis , 2015 .

[50]  T. Hughes,et al.  Efficient quadrature for NURBS-based isogeometric analysis , 2010 .

[51]  Roland Wüchner,et al.  A Nitsche‐type formulation and comparison of the most common domain decomposition methods in isogeometric analysis , 2014 .

[52]  M. Cox.  The Numerical Evaluation of B-Splines , 1972 .

[53]  Ekkehard Ramm,et al.  Hierarchic isogeometric large rotation shell elements including linearized transverse shear parametrization , 2017 .

[54]  P. Hansbo,et al.  An unfitted finite element method, based on Nitsche's method, for elliptic interface problems , 2002 .

[55]  Michael Breitenberger,et al.  CAD-Integrated Design and Analysis of Shell Structures , 2016 .

[56]  Eugenio Oñate,et al.  An Object-oriented Environment for Developing Finite Element Codes for Multi-disciplinary Applications , 2010 .