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As one of the earliest high-level programming languages, Fortran with easy accessibility and computational efficiency is widely used in the engineering field. The purpose of this paper is to present a Fortran implementation of isogeometric analysis (IGA) for thin plate problems.

IGA based on non-uniform rational B-splines (NURBS) offers exact geometries and is more accurate than finite element analysis (FEA). Unlike the basis functions in FEA, NURBS basis functions are non-interpolated. Hence, the penalty method is used to enforce boundary conditions.

Several thin plate examples based on the Kirchhoff-Love theory were illustrated to demonstrate the accuracy of the implementation in contrast with analytical solutions, and the efficiency was validated in comparison with another open method.

A Fortran implementation of NURBS-based IGA was developed to solve Kirchhoff-Love plate problems. It easily obtained high-continuity basis functions, which are necessary for Kirchhoff formulation. In comparison with theoretical solutions, the numerical examples demonstrated higher accuracy and faster convergence of the Fortran implementation. The Fortran implementation can well solve the time-consuming problem, and it was validated by the time-consumption comparison with the Matlab implementation. Due to the non-interpolation of NURBS, the penalty method was used to impose boundary conditions. A suggestion of the selection of penalty coefficients was given.

This study aims to accurately calculate the magnetic field distribution, which is a prerequisite for pre-design and optimization of electromagnetic performance. Accurate calculation of magnetic field distribution is a prerequisite for pre-design and optimization.

This paper proposes an analytical model of permanent magnet machines with segmented Halbach array (SHA-PMMs) to predict the magnetic field distribution and electromagnetic performance. The field problem is divided into four subdomains, i.e. permanent magnet, air-gap, stator slot and slot opening. The Poisson’s equation or Laplace’s equation of magnetic vector potential for each subdomain is solved. The field’s solution is obtained by applying the boundary conditions. The electromagnetic performances, such as magnetic flux density, unbalanced magnetic force, cogging torque and electromagnetic torque, are analytically predicted. Then, the influence of design parameters on the torque is explored by using the analytical model.

The finite element analysis and prototype experiments verify the analytical model’s accuracy. Adjusting the design parameters, e.g. segments per pole and air-gap length, can effectively increase the electromagnetic torque and simultaneously reduce the torque ripple.

The main contribution of this paper is to develop an accurate magnetic field analytical model of the SHA-PMMs. It can precisely describe complex topology, e.g. arbitrary segmented Halbach array and semi-closed slots, etc., and can quickly predict the magnetic field distribution and electromagnetic performance simultaneously.