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Purpose The purpose of this paper is to propose a new three-node triangular element in the framework of the numerical manifold method (NMM), which is designated by Trig3-MLScns.Design/methodology/approach The formulation uses the improved parametric shape functions of classical triangular elements (Trig3-0) to construct the partition of unity (PU) and the moving least square (MLS) interpolation method to construct the local approximation function.Findings Compared with the classical three-node element (Trig3-0), the Trig3-MLScns element has a higher order of approximations, much better accuracy and continuous nodal stress. Moreover, the linear dependence problem associated with many PU-based methods with high-order approximations is eliminated in the present element. A number of numerical examples indicate the high accuracy and robustness of the Trig3-MLScns element.Originality/value The proposed element inherits the individual merits of the NMM and the MLS. [ABSTRACT FROM AUTHOR]

Purpose The velocity head is usually neglected in the energy equation for a pipeline junction when one-dimensional (1D) hydraulic transient flow is solved by method of characteristics. The purpose of this paper is to investigate the effect of velocity head on filling transients in a branched pipeline by an energy equation considering velocity head.Design/methodology/approach An interface tracking method is used to locate the air–water interface during pipeline filling. The pressured pipe flow is solved by a method of characteristics. A discrete gas cavity model is included to permit the occurrence of column separation. A universal energy equation is built by considering the velocity head. The numerical method is provisionally verified in a series pipeline and the numerical results and experimental data accord well with each other.Findings The numerical results show that some differences in filling velocity and piezometric head occur in the branched pipeline. These differences arise because the velocity head in the energy equation can become an important contributor to the hydraulic response of the system. It is also confirmed that a local high point in the profile is apt to experience column separation during rapid filling. Significantly, the magnitude of overpressure and cavity volume induced by filling transients at the local high point is predicted to increase with the velocity in the pipes.Originality/value The velocity head in the energy equation for a pipeline junction could play an important role in the prediction of filling velocity, piezometric head and column separation phenomenon, which should be given more attention in 1D hydraulic transient analysis. [ABSTRACT FROM AUTHOR]

Purpose Metal plates are usually used as protective shields of engineering structures, which probably undergo multiple projectile impacts resulting from gunshot and blast. Though a large number of studies have been conducted on the performance of metal plates under a single projectile impact, few studies have explored their performance under multiple projectile impacts. This paper aims to explore the performance of Weldox 460 E steel plates against multiple projectile impacts through numerical simulation.Design/methodology/approach A three-dimensional coupled finite element (FE) and smoothed particle hydrodynamics (SPH) model was developed to simulate the perforation of a 12-mm-thick Weldox 460 E steel plate by an ogival projectile. The model was verified by existing experimental data. Then, it was extended to investigate the same target plate subjected to impacts with multiple projectiles. Simultaneous impacts with different number of projectiles, as well as sequential impacts with two projectiles, were considered.Findings Effects of spacing between projectiles on residual velocity of projectile, ballistic limit and failure mode of target were revealed for simultaneous impacts. Effects of spacing and axial distance between projectiles on residual velocity of projectile were explored for sequential impacts.Originality/value This work developed an advanced FE–SPH model to simulate perforation of steel plates by multiple projectiles, and revealed the effects of multiple impacts on ballistic performance of steel plates. It provides guidance for the design of protective structures/shields in various engineering applications. [ABSTRACT FROM AUTHOR]