A new concept called analysis in computer aided design (AiCAD) is proposed for design-through-analysis workflow. This concept uses non-uniform rational B-Splines (NURBS)-based B-Rep models for the ...entire workflow. Such models consist of trimmed NURBS surfaces and are considered standard in the industry, especially for modeling free-form geometries. The newly developed isogeometric B-Rep analysis (IBRA) used in AiCAD is also presented. IBRA can be considered as a generalization of isogeometric analysis (IGA) that uses the boundary representation (B-Rep) of the design model in addition to the same basis functions as in IGA for approximating the solution fields. IBRA provides the framework for creating a direct and complete analysis model from computer aided design (CAD) in a consistent finite-element-like manner. Thus, IBRA allows analyzing a CAD model without remodeling and meshing, even for complex geometries.
For the numerical integration of trimmed surfaces, the concept of nested Jacobian approach (NEJA) with NURBS surfaces is introduced. In addition, for enforcing the different types of boundary conditions or mechanical entities, a new finite element type called isogeometric B-Rep element is introduced. Elements of this type permit enforcing, e.g., coupling or Dirichlet boundary conditions. A corresponding formulation based on a penalty approach is presented as well.
The proposed workflow is realized exemplarily for surface modeling and the geometrical nonlinear analysis of shell structures. The differences between the standard analysis procedure and the AiCAD workflow are explained in detail. Various numerical examples confirm the accuracy, flexibility, and robustness of the proposed IBRA concept, thus highlighting its advantages for the realization of design-through-analysis workflow with a uniform geometry representation.
•The concept of isogeometric B-Rep analysis (IBRA) is introduced as extension of IGA.•IBRA is based on original CAD models (i.e. trimmed NUBRS based B-Rep models).•A new B-Rep element formulation to couple trimmed multi-patch shells is introduced.•The basis for an integrated design-through-analysis workflow is elaborated in detail.•Various benchmarks show the potential of IBRA (robustness, flexibility and accuracy)
In this paper we present an isogeometric formulation for rotation-free thin shell analysis of structures comprised of multiple patches. The structural patches are
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1- or higher-order continuous in ...the interior, and are joined with
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0-continuity. The Kirchhoff–Love shell theory that relies on higher-order continuity of the basis functions is employed in the patch interior as presented in Kiendl et al. 36. For the treatment of patch boundaries, a method is developed in which strips of fictitious material with unidirectional bending stiffness and zero membrane stiffness are added at patch interfaces. The direction of bending stiffness is chosen to be transverse to the patch interface. This choice leads to an approximate satisfaction of the appropriate kinematic constraints at patch interfaces without introducing additional stiffness to the shell structure. The attractive features of the method include simplicity of implementation and direct applicability to complex, multi-patch shell structures. The good performance of the bending strip method is demonstrated on a set of benchmark examples. Application to a wind turbine rotor subjected to realistic wind loads is also shown. Extension of the bending strip approach to the coupling of solids and shells is proposed and demonstrated numerically.
A Kirchhoff–Love shell element is developed on the basis of the isogeometric approach
16. NURBS as basis functions for analysis have proven to be very efficient and offer the great feature of exact ...geometric representation. For a Kirchhoff–Love shell element they additionally have the significant advantage that the necessary continuities between elements are easily achieved. The element is formulated geometrically nonlinear. It is discretized by displacement degrees of freedom only. Aspects related to rotational degrees of freedom are handled by the displacement control variables, too. A NURBS-based CAD program is used to model shell structures built up from NURBS and isogeometric analysis is performed on the same model without meshing. Different examples show the performance of this method and its applicability for the integration of design and analysis.
We present a consistent and efficient approach to the formulation of geometric nonlinear finite elements for isogeometric analysis (IGA) and isogeometric B-Rep analysis (IBRA) based on the adjoint ...method. IGA elements are computationally expensive, especially for high polynomial degrees. Using the method presented here enables us to reduce this disadvantage and develop a methodical framework for the efficient implementation of IGA elements. The elements are consistently derived from energy functionals. The load vector and stiffness matrix are obtained from the first and second order derivatives of the energy. Starting from the functional, we apply the concept of algorithmic or automatic differentiation to compute the precise derivatives. Here, we compare the direct (forward) and adjoint (reversed) methods. Analysis of the computational graph allows us to optimize the computation and identify recurring modules. It turns out that using the adjoint method leads to a core-congruential formulation, which enables a clean separation between the mechanical behavior and the geometric description. This is particularly useful in CAD-integrated analysis, where mechanical properties are applied to different geometry types. The adjoint method produces the same results but requires significantly fewer operations and fewer intermediate results. Moreover, the number of intermediate results is no longer dependent on the polynomial degree of the NURBS. This is important for implementation efficiency and computation speed.
The procedure can be applied to arbitrary element formulations and coupling conditions based on energy functionals. For demonstration purposes, we present the proposed approach specifically for use with geometrically nonlinear trusses, beams, membranes, shells, and coupling conditions based on the penalty method.
•Methodical framework for efficient implementation of isogeometric finite elements.•Separation between mechanical behavior and geometric description.•Increased performance with high polynomial degree.•Automated procedure based on algorithmic differentiation.•Analysis of computational graph to optimize computation.
•A novel monolithic method for ponding analysis on membrane structures is proposed.•Partitioned method can be used for ponding analysis with black box structural solver.•The proposed monolithic ...method was faster and more robust than the other methods.
This paper proposes monolithic and partitioned methods to calculate the static deformation of a membrane structure due to a given volume of ponding water. The partitioned methods involve coupling of a structural solver for membranes and a volume-conserving solver, modeling static incompressible fluid. Two methods of this type are proposed, either using coupling iterations with convergence accelerator between structural solver and volume-conserving solver or adding the linearized fluid behavior in the structural solver in addition to the external coupling iterations. The monolithic methods solve the system of structural equations under hydrostatic load with the volume conservation behavior of the fluid included in the Newton-Raphson (N-R) iterations of the structural solver. One such method was already discussed in the literature and updates the free surface plane to conserve volume exactly after every N-R iteration. In the second, new monolithic method, the volume conservation constraint is added as an additional equation and solved together with the structural equations. It was found that the partitioned method used with a quasi-Newton convergence accelerator was very robust but slower than the monolithic methods. On the other hand, the new monolithic method proposed in this paper was found to be both computationally efficient and robust.
Isogeometric B-Rep Analysis (IBRA) was the first approach that enabled a full integration of Computer Aided Design (CAD) and Computer Aided Engineering (CAE) based on trimmed NURBS B-Rep models ...ubiquitous in industrial CAD. However, the applicability of IBRA to explicit dynamic problems such as vehicle crash simulations and especially the effect of trimming and penalty coupling on the critical time step were not systematically investigated in the literature. To fill this gap, we developed Explicit IBRA, a combination of the patch coupling capabilities of IBRA with the explicit dynamic features of the FE solver LS-DYNA.
For Explicit IBRA, we particularly (i) developed a new penalty-based B-Rep element formulation for the application to a Reissner–Mindlin shell with six degrees of freedom, (ii) formally extended the IBRA theory to explicit time integration schemes, (iii) showed that the common stability criterion and the maximum eigenvalue-based time step estimation from FE still hold, and (iv) used the IBRA exchange format to implement a closed design workflow between the CAD program Rhinoceros and the solver LS-DYNA. We solved selected benchmark problems, from quasi-static linear elastic to highly dynamic elasto-plastic with large deformations, and obtained accurate results with penalty factors that cause no or only a minor decrease in stable time step size. That is, we found that penalty coupling does not have a severe impact on the critical time step in explicit analysis, making Explicit IBRA practically applicable. Finally, we studied an industrial BMW engine bonnet model under dynamic loading and observed good agreement with reference finite element simulations.
•We extend Isogeometric B-Rep Analysis (IBRA) to explicit dynamics: Explicit IBRA.•We present a new B-Rep element to couple rotation-based Reissner–Mindlin shells.•Explicit IBRA enables crash-type simulations on trimmed multi-patch NURBS models.•Accurate solutions & feasible time step size in trimmed, penalty-coupled benchmarks.•Explicit dynamic analysis on a trimmed multi-patch BMW engine bonnet model.
This paper proposes a coupling scheme for isogeometric elements, which is valid for large rotations and displacements. Two elements can be coupled not only at interpolated control points but also ...inside the parametric domain of a NURBS patch. Furthermore, each cross section may be arbitrarily oriented in space. The formulation is applicable for all structural elements, where an orthogonal system of base vectors can be derived. An Euler–Bernoulli beam is used as an example in order to illustrate the demands on the coupling conditions in the proposed approach. Moreover, the conditions are chosen such that different types of joints, e.g. scissor joints, can be modeled and such that they are easy and fast to implement. The coupling is incorporated by an additional term in the Principle of Virtual Work which is here computed using a penalty approach. The Euler–Bernoulli beam is summarized in order to introduce the notations in this contribution. This is followed by the proposed coupling conditions in the weak form. Subsequently, alternatives for the coupling conditions are briefly introduced. Eventually, benchmark and demonstrator examples validate and illustrate the proposed coupling methodology.
We present isogeometric shape optimization for shell structures applying sensitivity weighting and semi-analytical analysis. We use a rotation-free shell formulation and all involved geometry models, ...i.e., initial design, analysis model, optimization model, and final design use the same geometric basis, in particular NURBS. A sensitivity weighting scheme is presented which eliminates certain effects of the chosen discretization on the design update. A multilevel design approach is applied such that the design space can be chosen independently from the analysis space. The use of semi-analytical sensitivities allows having different polynomial degrees for design and analysis model. Different numerical examples are performed which confirm the applicability of the proposed method. Furthermore, a shape optimization example with an exact solution is presented which can serve as general benchmark for shape optimization methods.
The aeroelastic response of the generic DTU 10 MW horizontal-axis wind turbine blades is investigated employing a time-accurate CFD–CSD loose coupling approach. An FSI coupling approach is ...implemented and used to conduct the aeroelastic simulations. The block-structured CFD solver FLOWer is employed to obtain the aerodynamic blade loads based on the time-accurate solution of the URANS equations. The CSD solver Carat++ is utilized to calculate the elastic deformations based on non-linear Timoshenko beam elements. Due to the rotor elasticity, the wind turbine power and thrust are increased by approximately 1% and 0.3% respectively. That increase is due to the large edgewise deformations which make the radial force component contribute to the rotor torque. Due to the presence of the tower in the coupled simulations, the forces and the deformations are reduced while the blades are crossing the tower. A time delay in the structural response due to the forces reduction causes a phase shift of 30°between the deformations reduction and the forces reduction. Also, the 1P amplitude of the wind turbine is reduced due to the blade flexibility by 6%, 12% and 22% at r∕R=0.3, 0.6 and 0.9 respectively.
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