Trivariate Isogeometric Analysis for Flexible Multibody Dynamics

Parallel isogeometric boundary element analysis with T-splines on CUDA

An isogeometric analysis (IGA) framework is presented to construct and solve dispersion relations for generating the band structure of periodic materials with complicated geometries representing phononic crystals and elastic metamaterials. As the dispersive properties depend on the microstructural geometry, an accurate representation of microstructural geometrical features is paramount. To this end, the ability of isogeometric analysis to exactly model complex curved geometries is exploited, and wave propagation in infinitely periodic solids is combined with isogeometric analysis. The benefits of IGA are demonstrated by comparing the results to those obtained using standard finite element analysis (FEA). It is shown that the IGA solutions can reach the same level of accuracy as FEA while using significantly fewer degrees of freedom. IGA is applied to phononic crystals and elastic metamaterials and the band structure for a variety of unit cells with complex microstructural geometries is investigated to illustrate the desirable dispersive effects in these metamaterials.

ABSTRACTThis paper aims to optimize both the topology of microstructure and macrostructure, by using the Moving Iso‐ Surface Threshold (MIST) method under the framework of Isogeometric Analysis (IGA). To achieve this, the physical response and the equivalent properties of the microstructure are solved by IGA. The physical response functions are defined at the control points. The NURBS fitting method is used to fit the physical response function, generating a NURBS surface for describing the physical response function, that is, the explicitly described physical response function surface. An iso‐surface cut the NURBS physical response surfaces to obtain the explicitly described structure topology. In addition, the standard IGS files of the NURBS physical response surface and iso‐surface can be transferred to Computer‐Aided‐Design (CAD) software without post‐processing. The multiscale structure can be easily assembled in CAD software using the proposed method. Finally, several numerical examples are performed to demonstrate the effectiveness and efficiency of the proposed method. Obtained results show good agreement with examples in literature in terms of both topology and final value of objective function.

Tensor-decomposition based matrix computation: A fast method for the isogeometric FSDT analysis of laminated composite plate

Isogeometric analysis (IGA) offers significant improvement in geometric accuracy over finite element analysis (FEA) by utilizing non-uniform rational B-spline (NURBS) basis functions, which allow a precise representation of complex geometries. Within the IGA framework, the robustness and efficiency of contact formulations can be further improved by refining contact surfaces using higher-order NURBS functions. This paper presents a contact surface enrichment strategy based on a varying-order NURBS discretization for three-dimensional (3D) frictional large deformation contact problems. The strategy enhances contact surface resolution, keeping the overall computational cost low by avoiding unnecessary refinement in non-contact regions. It also achieves better accuracy and efficiency in capturing complex contact behavior, making it a promising framework for solving general 3D frictional large deformation contact problems. A detailed algorithm is provided to facilitate user implementation. A comprehensive set of numerical examples is also presented to show the effectiveness of the strategy.

Isogeometric Analysis (IgA) is an emerging numerical procedure conceived as a useful advancement of the traditional Finite Element Method (FEM). The essence of IgA is to bridge the current communication gap between Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) modules by employing high-order smooth spline basis functions both for geometry modelling and the construction of the solution space of analysis. As such, the method enables major benefits, namely a simplified pre-processing workflow and enhanced accuracy per degree of freedom associated with the capability of by-passing the time-consuming mesh creation stage and preserving exact geometry regardless of grid refinement. Furthermore, a user’s prerogative of selecting bases with adequate interelement continuity allows for a direct discretization of high-order differential operators, thereby avoiding stress recovery algorithms at the patch level during post-processing. In this contribution, the isogeometric approach is introduced to the detailed analysis of a ship’s structural member. In this regard, an in-house MatLab code has been developed for the structural assessment of linearly elastic isotropic continua, defined by either one or multiple NURBS patches. Within the IgA framework, the displacement approach of the mechanical problem is treated in its equivalent weak form and the obtained variational statement is discretized by means of an isogeometric Navier solid element formulation. Patch tests, involving in-plane loaded steel plates, are preliminarily performed to verify the accuracy of the numerical prediction, delivered by the present code, with respect to its analytical counterpart. A typical T-beam with associated plating is then analysed under uniform loading. It is demonstrated that the proposed approach can be recommended for engineering practice.

An ultra-accurate isogeometric dynamic analysis is presented. The key ingredient of the proposed methodology is the development of isogeometric higher order mass matrix. A new one-step method is proposed for the construction of higher order mass matrix. In this approach, an adjustable mass matrix is formulated through introducing a set of mass parameters into the consistent mass matrix under the element mass conservation condition. Then the semi-discrete frequency derived from the free vibration equation with the adjustable mass matrix is served as a measure to optimize the mass parameters. In 1D analysis, it turns out that the present one-step method can perfectly recover the existing reduced bandwidth mass matrix and the higher order mass matrix by choosing different mass parameters. However, the employment of the proposed one-step method to the 2D membrane problem yields a remarkable gain of solution accuracy compared with the higher order mass matrix generated by the original two-step method. Subsequently a full-discrete isogeometric transient analysis algorithm is presented by using the Newmark time integration scheme and the higher order mass matrix. The full-discrete frequency is derived to assess the accuracy of space-time discretization. Finally a set of numerical examples are presented to evaluate the accuracy of the proposed method, which show that very favorable solution accuracy is achieved by the present dynamic isogeometric analysis with higher order mass formulation compared with that obtained from the standard consistent mass approach.

An efficient model reduction method for buckling analyses of thin shells based on IGA

PurposeNumerical instability such as spurious oscillation is an important problem in the simulation of heat wave propagation. The purpose of this study is to propose a time discontinuous Galerkin isogeometric analysis method to reduce numerical instability of heat wave propagation in the medium subjected to heat sources, particularly heat impulse.Design/methodology/approachThe essential vectors of temperature and the temporal gradients are assumed to be discontinuous and interpolated individually in the discretized time domain. The isogeometric analysis method is applied to use its property of smooth description of the geometry and to eliminate the mesh-dependency. An artificial damping scheme with proportional stiffness matrix is brought into the final discretized form to reduce the numerical spurious oscillations.FindingsThe numerical spurious oscillations in the simulation of heat wave propagation are effectively eliminated. The smooth description of geometry with spline functions solves the mesh-dependency problem and improves the numerical precision.Originality/valueThe time discontinuous Galerkin method is applied within the isogeometric analysis framework. The proposed method is effective in the simulation of the wave propagation problems subjecting to impulse load with numerical stability and accuracy.

Isogeometric analysis of laminated composite and functionally graded sandwich plates based on a layerwise displacement theory

Isogeometric analysis of insoluble surfactant spreading on a thin film

An isogeometric analysis formulation for red blood cell electro-deformation modeling

Isogeometric analysis (IGA) has been implemented to solve the electric field integral equation (EFIE) on simply-connected subdivision surfaces (Li et al., J. Comput. Phys., 319, 145–162, 2016) using a Helmholtz decomposition. This paper will present a method of moments within the framework of IGA on more complicated (mainly multiply-connected) subdivision surfaces by developing div-conforming basis sets. Furthermore, we will examine h-refinement to study the super-convergence behavior of the numerical scheme used to discretize the the EFIE.

Adaptive isogeometric multi-material topology optimization based on suitably graded truncated hierarchical B-spline

An isogeometric Burton-Miller method for the transmission loss optimization with application to mufflers with internal extended tubes