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In this paper, a novel locking-free finite beam element is proposed utilizing the absolute nodal coordinate formulation. By incorporating a gradient vector along the transverse direction at the boundary points, the linear interpolation of the gradient vector field within this element is achieved. Consequently, the problem of constant transverse strain distribution, which is observed in the Omar–Shabana beam element, is effectively addressed. Building upon this concept, this study further extends the proposed element from two dimensions to three dimensions. Additionally, it analyzes and compares the locking alleviation mechanism of the newly developed element and Patel–Shabana beam element. The analysis aims to provide insights into the factors contributing to the locking alleviation of different absolute nodal coordinate formulation (ANCF) elements. Furthermore, to demonstrate the effectiveness of the new element, six numerical simulation examples are designed, comprising three and three dynamic examples. These examples encompass small deformation statics, large deformation statics, small-scale motion, large-scale motion, and rotational motion problems. Finally, the results indicate that the proposed ANCF beam element can effectively alleviate the locking problem. The element exhibits robust adaptability, rationality, and effectiveness when subjected to complex mechanical characteristics by comparing the numerical results of this element with the classical Omar–Shabana, high-order Shen, and Patel–Shabana elements. [ABSTRACT FROM AUTHOR]

In this paper, we propose a computational method for rapidly estimating the gravitational acceleration of irregular asteroids: the pseudocenter theory, triangular mesh, kriging interpolation (PTK) method. The method first uses a triangular mesh to discretize the asteroid's surface. Then, the fitting coefficients of all grid point directions are obtained using pseudocenter theory. Finally, kriging interpolation is used to quickly estimate the gravitational acceleration value at any location. Numerical simulation shows that the PTK method can ensure a high calculation speed, wide application range, and high accuracy with an extremely low storage cost. Overall, the PTK method is more balanced, faster, and more feasible than current methods for calculating gravitational acceleration for on-orbit use. [ABSTRACT FROM AUTHOR]

In this paper, we propose an extended aperture direction-of-arrival (DOA) estimation algorithm using a coprime acoustic vector sensor array. Each acoustic vector sensor consists of one pressure sensor and one uniaxial velocity sensor, collocated in a single point in space. By full utilization of both pressure and particle-velocity information in the acoustic wavefield, the whole coarray output is shown to be treated as four pressure–velocity (p–v) components. In this way, array interpolation and Toeplitz matrix reconstruction are performed on each of the four p–v components to exploit the entire coarray aperture. After interpolation, DOA estimates are derived in closed form using the interpolated coarray data. The proposed algorithm allows the inter-sensor spacing of the interpolated coarray to be significantly greater than half a wavelength, thereby achieving aperture extension without needing extra sensors. Moreover, it enables provide the unambiguous DOA estimates with high accuracy, despite the phase aliasing caused by aperture extension. All these advantages are not offered by the existing coprime array DOA estimation algorithms. Finally, computer simulations are carried out to verify the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

We present and analyse the performance of different combinations of four higher-order numerical integrators and up to nine interpolation schemes applied to the problem involving the Sun and four Gas-giants (outer planets), namely, Jupiter, Saturn, Uranus, and Neptune. The Hermite interpolation schemes obtained by one, two, and three time-step and interpolants for ODEX2 and ERKN integrators are considered in this paper. The interpolants are a special example of an interpolation scheme, which produce an approximation that is continuous across one step and across the complete interval of integration. The interpolants are quite expensive in comparison with the other interpolation schemes. Therefore, one of the objectives of this paper is to investigate the possibilities of replacing the interpolants of certain integrators by other interpolation schemes, perhaps at a cost of a little bit of accuracy. The experiments are performed to examine the error growth in the positions, velocities, and relative error in energy and angular momentum using different combinations of integrators and interpolation schemes over a long interval of integration, as long as 100 million years for the Jovian problem with local error tolerances ranging from 10-16 to 10-08. [ABSTRACT FROM AUTHOR]

In this paper, an effective diffusion coefficient derived from previous semi-empirical formula and dynamic grid technology combined with inverse distance interpolation algorithm are applied to simulate wind-induced snow drifting on low-sloped gable roofs. The effective diffusion coefficient enhances the diffusion ability of particles near the wall surface, and the inverse distance interpolation algorithm has an explicit format, which determines the influence of the sample point on the interpolation point according to the interpolation distance, it has a low computational expense and weakens the influence of extreme points. Two measurement parameters, δ H and δ M , are introduced to illustrate the impact of interpolation parameters (power law p and interpolation radius R) on the single grid adjustment and snow cover. By employing these optimisations, sensitivity analyses for simulation parameters are performed, the effects of the saltation layer height, turbulent Schmidt number, falling velocity, time step size, and wind duration on snow distribution are discussed. Finally, the redistributions of snow cover on gable roofs under various wind directions are reproduced, the snow redistribution characteristics and the relationship between roof slope and snow erosion are investigated. The results can provide a reference for predicting snow loads on gable roofs. • A numerical simulation method with a revised diffusion term is proposed, which can enhance the diffusion ability of particles near the wall surface effectively. • This method and simulation parameters are validated by scaled model experiments. • The impact of simulation parameters is analysed in details. • The redistributions of snow cover on gable roofs under various wind directions are reproduced, the snow redistribution characteristics are investigated. [ABSTRACT FROM AUTHOR]

This paper presents a family of numerical solvers for anisotropic subdiffusion problems in annuli and also cylindrical and spherical shells. The fractional order Caputo temporal derivative is discretized based on linear interpolation. The spatial Laplacian is discretized by utilizing Chebyshev and Fourier spectral collocation. Detailed discussion and useful formulas are presented for polar, cylindrical, and spherical coordinate systems. Numerical experiments along with a brief analysis are presented to demonstrate the accuracy and efficiency of these solvers. These solvers represent a continuation of our work in Tan and Liu (2020) and shall be useful for numerical simulations of subdiffusion problems in cellular cytoplasm and other similar settings. [ABSTRACT FROM AUTHOR]