A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the ...A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the context of nonlocal operators.The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity,which is necessary for the eigenvalue analysis such as the waveguide problem.The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields.The governing equations are converted into nonlocal integral form.An hourglass energy functional is introduced for the elimination of zeroenergy modes.Finally,the proposed method is validated by testing three classical benchmark problems.展开更多
A dual-support smoothed particle hydrodynamics(DS-SPH)that allows variable smoothing lengths while satisfying the conservations of linear momentum,angular momentum and energy is developed.The present DS-SPH is inspire...A dual-support smoothed particle hydrodynamics(DS-SPH)that allows variable smoothing lengths while satisfying the conservations of linear momentum,angular momentum and energy is developed.The present DS-SPH is inspired by the dual-support,a concept introduced from dual-horizon peridynamics from the authors and applied here to SPH so that the unbalanced interactions between the particles with different smoothing lengths can be correctly considered and computed.Conventionally,the SPH formulation employs either the influence domain or the support domain.The concept of dual-support identifies that the influence domain and the support domain involves the duality and should be simultaneously in the SPH formulation when variable smoothing lengths are used.The DS-SPH formulation can be implemented into conventional SPH codes with minimal changes and also without compromising the computational efficiency.A number of numerical examples involving weakly compressible.fluid are presented to demonstrate the capability of the method.展开更多
The desire to benefit from economy of scale is one of the major driving forces behind the continuous growth in ship sizes. However, models of new large ships need to be thoroughly investigated to determine the carrier...The desire to benefit from economy of scale is one of the major driving forces behind the continuous growth in ship sizes. However, models of new large ships need to be thoroughly investigated to determine the carrier's response in waves. In this work, experimental and numerical assessments of the motion and load response of a 550,000 DWT ore carrier are performed using prototype ships with softer stiffness, and towing tank tests are conducted using a segmented model with two schemes of softer stiffness. Numerical analyses are performed employing both rigid body and linear hydroelasticity theories using an in-house program and a comparison is then made between experimental and numerical results to establish the influence of stiffness on the ore carrier's springing response. Results show that softer stiffness models can be used when studying the springing response of ships in waves.展开更多
We consider a vertical circular cylinder on which the vertical variation of water diffraction waves is to be represented by a series of Laguerre functions ?using Laguerre Polynomials . The variation is assumed to be o...We consider a vertical circular cylinder on which the vertical variation of water diffraction waves is to be represented by a series of Laguerre functions ?using Laguerre Polynomials . The variation is assumed to be of the form ?with the integer n depending on the radius of cylinder. Generally, the integer n increases for a cylinder of larger diameter. The usual approximation by Laguerre functions is extended by introducing a scale parameter. The convergence of Laguerre series is then dependent on the value of the scale parameter s. The analytical and numerical computations of series coefficients are performed to study the number of series terms to keep the same accuracy. Indeed, the choice of integer n depends on the scale parameter. Furthermore, diffraction waves generated by a semi-sphere inside the cylinder are evaluated on the cylinder surface. It is shown that the approximation by Laguerre series for diffraction waves on the cylinder is effective. This work provides important information for the choice of the radius of control surface in the domain decomposition method for solving hydrodynamic problems of body-wave interaction.展开更多
We consider the problem of a ship advancing in waves. In this method, the zone of free surface in the vicinity of body is discretized. On the discretized surface, the first-order and second-order derivatives of ship w...We consider the problem of a ship advancing in waves. In this method, the zone of free surface in the vicinity of body is discretized. On the discretized surface, the first-order and second-order derivatives of ship waves are represented by the B-Spline formulae. Different ship waves are approximated by cubic B-spline and the first and second order derivates of incident waves are calculated and compared with analytical value. It approves that this numerical method has sufficient accuracy and can be also applied to approximate the velocity potential on the free surface.展开更多
文摘A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the context of nonlocal operators.The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity,which is necessary for the eigenvalue analysis such as the waveguide problem.The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields.The governing equations are converted into nonlocal integral form.An hourglass energy functional is introduced for the elimination of zeroenergy modes.Finally,the proposed method is validated by testing three classical benchmark problems.
基金The authors acknowledge the supports from the ERC-CoG(Computational Modeling and Design of Lithium-ion Batteries(COMBAT)),RISE-BESTOFRAC and National Science Foundation of China(51474157).
文摘A dual-support smoothed particle hydrodynamics(DS-SPH)that allows variable smoothing lengths while satisfying the conservations of linear momentum,angular momentum and energy is developed.The present DS-SPH is inspired by the dual-support,a concept introduced from dual-horizon peridynamics from the authors and applied here to SPH so that the unbalanced interactions between the particles with different smoothing lengths can be correctly considered and computed.Conventionally,the SPH formulation employs either the influence domain or the support domain.The concept of dual-support identifies that the influence domain and the support domain involves the duality and should be simultaneously in the SPH formulation when variable smoothing lengths are used.The DS-SPH formulation can be implemented into conventional SPH codes with minimal changes and also without compromising the computational efficiency.A number of numerical examples involving weakly compressible.fluid are presented to demonstrate the capability of the method.
基金Supported by the National Natural Science Foundation of China （Grant No. 51079034）, and the National Basic Research Program of China （Grant No. 2011CB013703）
文摘The desire to benefit from economy of scale is one of the major driving forces behind the continuous growth in ship sizes. However, models of new large ships need to be thoroughly investigated to determine the carrier's response in waves. In this work, experimental and numerical assessments of the motion and load response of a 550,000 DWT ore carrier are performed using prototype ships with softer stiffness, and towing tank tests are conducted using a segmented model with two schemes of softer stiffness. Numerical analyses are performed employing both rigid body and linear hydroelasticity theories using an in-house program and a comparison is then made between experimental and numerical results to establish the influence of stiffness on the ore carrier's springing response. Results show that softer stiffness models can be used when studying the springing response of ships in waves.
文摘We consider a vertical circular cylinder on which the vertical variation of water diffraction waves is to be represented by a series of Laguerre functions ?using Laguerre Polynomials . The variation is assumed to be of the form ?with the integer n depending on the radius of cylinder. Generally, the integer n increases for a cylinder of larger diameter. The usual approximation by Laguerre functions is extended by introducing a scale parameter. The convergence of Laguerre series is then dependent on the value of the scale parameter s. The analytical and numerical computations of series coefficients are performed to study the number of series terms to keep the same accuracy. Indeed, the choice of integer n depends on the scale parameter. Furthermore, diffraction waves generated by a semi-sphere inside the cylinder are evaluated on the cylinder surface. It is shown that the approximation by Laguerre series for diffraction waves on the cylinder is effective. This work provides important information for the choice of the radius of control surface in the domain decomposition method for solving hydrodynamic problems of body-wave interaction.
文摘We consider the problem of a ship advancing in waves. In this method, the zone of free surface in the vicinity of body is discretized. On the discretized surface, the first-order and second-order derivatives of ship waves are represented by the B-Spline formulae. Different ship waves are approximated by cubic B-spline and the first and second order derivates of incident waves are calculated and compared with analytical value. It approves that this numerical method has sufficient accuracy and can be also applied to approximate the velocity potential on the free surface.
