In this paper,we consider the Neumann problem for special Lagrangian equations with critical phase.The global gradient and Hessian estimates are obtained.Using the method of continuity,we prove the existence of soluti...In this paper,we consider the Neumann problem for special Lagrangian equations with critical phase.The global gradient and Hessian estimates are obtained.Using the method of continuity,we prove the existence of solutions to this problem.展开更多
Based on the three-order Lagrangian equations, Hamilton's function of acceleration H^* and generalized acceleration momentum P^*α are defined, and pseudo-Hamilton canonical equations corresponding to three-order L...Based on the three-order Lagrangian equations, Hamilton's function of acceleration H^* and generalized acceleration momentum P^*α are defined, and pseudo-Hamilton canonical equations corresponding to three-order Lagrangian equations are obtained. The equations are similar to Hamilton's canonical equations of analytical mechanics in form.展开更多
With the incorporation of total Lagrangian smoothed particle hydrodynamics(SPH) method equation and moving least square(MLS) function,the traditional SPH method is improved regarding the stability and consistency....With the incorporation of total Lagrangian smoothed particle hydrodynamics(SPH) method equation and moving least square(MLS) function,the traditional SPH method is improved regarding the stability and consistency.Based on Mindlin-Ressiner plate theory,the SPH method simulating dynamic behavior via one layer of particles is applied to plate's mid-plane,i.e.,a SPH shell model is constructed.Finally,through comparative analyses on the dynamic response of square,stiffened shells and cylindrical shells under various strong impact loads with common finite element software,the feasibility,validity and numerical accuracy of the SPH shell method are verified.Consequently,further researches on SPH shell may well pave the way towards solving problems involving dynamic plastic damage,tearing or even crushing.展开更多
Establishing the Lagrangian equation of double complex pendulum system and obtaining the dynamic differential equation,we can analyze the motion law of double compound pendulum with application of the numerical simula...Establishing the Lagrangian equation of double complex pendulum system and obtaining the dynamic differential equation,we can analyze the motion law of double compound pendulum with application of the numerical simulation of RK-8 algorithm.When the double compound pendulum swings at a small angle,the Lagrangian equation can be simplified and the normal solution of the system can be solved.And we can walk further on the relationship between normal frequency and swing frequency of double pendulum.When the external force of normal frequency is applied to the double compound pendulum,the forced vibration of the double compound pendulum will show the characteristics of beats.展开更多
Owing to its ability of modelling large deformations and the ease of dealing with moving boundary conditions,the material point method is gaining popularity in geotechnical engineering applications.In this paper,this ...Owing to its ability of modelling large deformations and the ease of dealing with moving boundary conditions,the material point method is gaining popularity in geotechnical engineering applications.In this paper,this promising Lagrangian method is applied to hydrodynamic problems to further explore its potential.The collapse of water columns with different initial aspect ratios is simulated by the material point method.In order to test the accuracy and stability of the material point method,simulations are first validated using experimental data and results of mature numerical models.Then,the model is used to ascertain the critical aspect ratio for the widely-used shallow water equations to give satisfactory approximation.From the comparisons between the simulations based on the material point method and the shallow water equations,the critical aspect ratio for the suitable use of the shallow water equations is found to be 1.展开更多
文摘In this paper,we consider the Neumann problem for special Lagrangian equations with critical phase.The global gradient and Hessian estimates are obtained.Using the method of continuity,we prove the existence of solutions to this problem.
文摘Based on the three-order Lagrangian equations, Hamilton's function of acceleration H^* and generalized acceleration momentum P^*α are defined, and pseudo-Hamilton canonical equations corresponding to three-order Lagrangian equations are obtained. The equations are similar to Hamilton's canonical equations of analytical mechanics in form.
基金supported by the Llyod’s Register Educational Trust (The LRET)the National Natural Science Foundation of China (50939002)the Excellent Young Scientists Fund (51222904)
文摘With the incorporation of total Lagrangian smoothed particle hydrodynamics(SPH) method equation and moving least square(MLS) function,the traditional SPH method is improved regarding the stability and consistency.Based on Mindlin-Ressiner plate theory,the SPH method simulating dynamic behavior via one layer of particles is applied to plate's mid-plane,i.e.,a SPH shell model is constructed.Finally,through comparative analyses on the dynamic response of square,stiffened shells and cylindrical shells under various strong impact loads with common finite element software,the feasibility,validity and numerical accuracy of the SPH shell method are verified.Consequently,further researches on SPH shell may well pave the way towards solving problems involving dynamic plastic damage,tearing or even crushing.
基金NUIST’s curriculum reform project of“integration of specialty and innovation”.
文摘Establishing the Lagrangian equation of double complex pendulum system and obtaining the dynamic differential equation,we can analyze the motion law of double compound pendulum with application of the numerical simulation of RK-8 algorithm.When the double compound pendulum swings at a small angle,the Lagrangian equation can be simplified and the normal solution of the system can be solved.And we can walk further on the relationship between normal frequency and swing frequency of double pendulum.When the external force of normal frequency is applied to the double compound pendulum,the forced vibration of the double compound pendulum will show the characteristics of beats.
基金supported by the European Union Seventh Framework Program(FP7/2007-2013)under grant agreement No.PIAG-GA-2012-324522“MPM-DREDGE”
文摘Owing to its ability of modelling large deformations and the ease of dealing with moving boundary conditions,the material point method is gaining popularity in geotechnical engineering applications.In this paper,this promising Lagrangian method is applied to hydrodynamic problems to further explore its potential.The collapse of water columns with different initial aspect ratios is simulated by the material point method.In order to test the accuracy and stability of the material point method,simulations are first validated using experimental data and results of mature numerical models.Then,the model is used to ascertain the critical aspect ratio for the widely-used shallow water equations to give satisfactory approximation.From the comparisons between the simulations based on the material point method and the shallow water equations,the critical aspect ratio for the suitable use of the shallow water equations is found to be 1.