Fracture Modelling of a Cracked Pressurized Cylindrical Structure by Using Extended Iso-Geometric Analysis (X-IGA)

In this study, a NURBS basis function-based extended iso-geometric analysis (X-IGA) has been implemented to simulate a two-dimensional crack in a pipe under uniform pressure using MATLAB code. Heaviside jump and asymptotic crack-tip enrichment functions are used to model the crack’s behaviour. The accuracy of this investigation was ensured with the stress intensity factors (SIFs) and the J-integral. The X-IGA—based SIFs of a 2-D pipe are compared using MATLAB code with the conventional finite element method available in ABAQUS FEA, and the extended finite element method is compared with a user-defined element. Therefore, the results demonstrate the possibility of using this technique as an alternative to other existing approaches to modeling cracked pipelines.

Analysis of Generic IGBEM for Lifting Hydrofoils

Today the most crucial aspect in the preliminary vessel design stage is to make it as green/blue as possible. One of the exciting goals is the minimisation of vessel resistance. The use of hydrofoils to reduce the vessel draught and consequently, reduction in the vessel resistance is today one of the hottest design topics, especially for catamaran passenger vessels. In the present work, we discuss the issues related to the implementation of Isogeometric Analysis (IGA) Boundary Element Method (BEM) for the calculation of the hydrodynamic properties of lifting hydrofoils. The use of IGBEM allows numerical calculation of foil hydrodynamic properties without the traditional step of mesh generation using the CAD geometry directly. The analysis relies on the NURBS basis function with the generic Galerkin approach allowing identical solutions procedures for 2D or 3D problems. Method accuracy and computational times for a different number of Degrees of Freedom (DOF) in 2D are investigated.

ENHANCED MESHFREE RPIM WITH NURBS BASIS FUNCTION FOR ANALYSIS OF IRREGULAR BOUNDARY DOMAIN

Radial Point Interpolation Method (RPIM) has become a powerful tool to numerical analysis due to its ability to provide a higher-order approximation function with the Kronecker delta property, by which the field nodes can be fitted exactly. However, one of the major drawbacks of RPIM is the inefficiency in handling irregular domain problems. This paper presents an enhanced RPIM formulation that employs Non-Uniform Rational B-Splines (NURBS) basis functions to represent the exact geometry of the boundary domain. The NURBS is a mathematical model which provides an efficient and numerically stable algorithm to exactly represent all conic sections in engineering modelling. Taking advantage of the flexibility and adaptivity of RPIM approximation and the accuracy of geometric representations by NURBS, this new method is able to improve geometry accuracy and flexibility in numerical analysis, thus providing a better and more rational approach to analyze irregular domain problems. Numerical problem of steady heat transfer considering curved beam is presented to verify the validity and accuracy of the developed method. The essential boundary condition can simply be imposed using direct imposition as in Finite Element Method (FEM). The result shows that the RPIM/NURBS achieved the converged solution much faster than conventional RPIM and FEM, with the number of nodes required only less than 200 for an error of less than 0.01%. This shows the potential of the developed method as a powerful numerical technique for future development.

The High Precision Blade Electrochemical Machining Simulation and Cathode Optimization Based on Isogeometric Method

The simulation and optimization of electrochemical machining is an important means to improve processing quality. However, the fragmented nature of geometric modeling and numerical analysis model, restricts the application proportion. Aiming at this problem, it is refined that the scientific problem of coordination modeling between CAD and CAE based isogeometric method. In this paper, the unified model is established based NURBS basis functions to solve the problems that the geometric parameterization and the infliction of boundary conditions. And the optimization efficiency is promoted by improved optimization model using the convex hull characteristic of NURBS basis function. At last, a confluent design method is realized for the blade electrochemical machining process.

ISOGEOMETRIC SIMULATION FOR BUCKLING, FREE AND FORCED VIBRATION OF ORTHOTROPIC PLATES

Buckling, free and forced vibration analyses of orthotropic plates are studied numerically using Isogeometric analysis. The present formulation is based on the classical plate theory (CPT) while the NURBS basis function is employed for both the parametrization of the geometry and the approximation of plate deflection. An efficient and easy-to-implement technique is used for imposing the essential boundary conditions. Numerical examples for free and forced vibration and buckling of orthotropic plates with different boundary conditions and configurations are considered. The numerical results are compared with other existing solutions to show the efficiency and accuracy of the proposed approach for such problems.

Isogeometric Analysis of Heat Transfer in Fluids

This paper is devoted to the numerical simulation of heat transfer in fluids. We develop a numerical formulation based on isogeometric analysis that permits straightforward construction of higher order smooth NURBS approximation. Firstly, we introduce the partial differential equation (PDE) which servers as basis for the whole paper. Then, we introduce Lagrange multiplier method to deal with essentional boundary contions accroding to the nature of NURBS basis function. After getting the Equivalent integral equation, the isogeometric solving format is established based on the idea of isoparametric which is the necessary fundamentals of Isogeometric Analysis. We also discuss the programming algorithm of isogeometric analysis based on Matlab. Finally, a numerical example in two dimensions is presented that illustrate the effectiveness and robustness of our approach.