The suitability of six higher order root solvers is examined for solving the nonlinear equilibrium equations in large deformation analysis of structures.The applied methods have a better convergence rate than the quad...The suitability of six higher order root solvers is examined for solving the nonlinear equilibrium equations in large deformation analysis of structures.The applied methods have a better convergence rate than the quadratic Newton-Raphson method.These six methods do not require higher order derivatives to achieve a higher convergence rate.Six algorithms are developed to use the higher order methods in place of the Newton-Raphson method to solve the nonlinear equilibrium equations in geometrically nonlinear analysis of structures.The higher order methods are applied to both continuum and discrete problems(spherical shell and dome truss).The computational cost and the sensitivity of the higher order solution methods and the Newton-Raphson method with respect to the load increment size are comparatively investigated.The numerical results reveal that the higher order methods require a lower number of iterations that the Newton-Raphson method to converge.It is also shown that these methods are less sensitive to the variation of the load increment size.As it is indicated in numerical results,the average residual reduces in a lower number of iterations by the application of the higher order methods in the nonlinear analysis of structures.展开更多
The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example ...The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example problems from the fracture mechanics literature(with available analytical solutions) including center slant crack in an infinite and finite body, single and double edge cracks, cracks emanating from a circular hole. The numerical values of Mode Ⅰ and Mode Ⅱ SIFs for these problems using HODDM are in excellent agreement with analytical results(reaching up to 0.001% deviation from their analytical results). The HODDM is also compared with the XFEM and a modified XFEM results. The results show that the HODDM needs a considerably lower computational effort(with less than 400 nodes) than the XFEM and the modified XFEM(which needs more than 10000 nodes) to reach a much higher accuracy. The proposed HODDM offers higher accuracy and lower computation effort for a wide range of problems in LEFM.展开更多
A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity poten...A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.展开更多
In this paper a framework for efficient irregular wave simulations using Higher Order Spectral method coupled with fully nonlinear viscous,two-phase Computational Fluid Dynamics(CFD)model is presented.CFD model is bas...In this paper a framework for efficient irregular wave simulations using Higher Order Spectral method coupled with fully nonlinear viscous,two-phase Computational Fluid Dynamics(CFD)model is presented.CFD model is based on solution decomposition via Spectral Wave Explicit Navier-Stokes Equation method,allowing efficient coupling with arbitrary potential flow solutions.Higher Order Spectrum is a pseudo-spectral,potential flow method for solving nonlinear free surface boundary conditions up to an arbitrary order of nonlinearity.It is capable of efficient long time nonlinear propagation of arbitrary input wave spectra,which can be used to obtain realistic extreme waves.To facilitate the coupling strategy,Higher Order Spectrum method is implemented in foam-extend alongside the CFD model.Validation of the Higher Order Spectrum method is performed on three test cases including monochromatic and irregular wave fields.Additionally,the coupling between Higher Order Spectrum and CFD is validated on three hour irregular wave propagation.Finally,a simulation of a 3D extreme wave encountering a full scale container ship is shown.展开更多
A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simp...A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.展开更多
The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid.The wavy shaped enclos...The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid.The wavy shaped enclosure is equipped with onequarter of a conducting solid cylinder.The system of equations resulting from the mathematical modeling of the physical problem in its dimensionless form is discretized via the higher-order Galerkin-based finite element method(GFEM).The dependency of various factors and their interrelationships affecting the hydro-thermal behavior and heat exchange rate are delineated.The numerical experiments reveal that the best heat transfer rate is achieved for the pseudo-plastic hybrid nanoliquid with high Rayleigh number and thermal conductivity ratio and low Hartmann number.Besides,the power-law index has a major effect in deteriorating the heat convection at high Rayleigh number.展开更多
In this paper, we develop a new technique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary differential equations. We call it a new method because we only see add...In this paper, we develop a new technique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary differential equations. We call it a new method because we only see additive extrapolation method before. This new method has a great advantage over additive extrapolation method because it keeps group property. If this method is used to construct higher order schemes from lower symplectic schemes, the higher order ones are also symplectic. First we introduce the concept of adjoint methods and some of their properties. We show that there is a self-adjoint scheme corresponding to every method. With this self-adjoint scheme of lower order, we can construct higher order schemes by multiplicative extrapolation method, which can be used to construct even much higher order schemes. Obviously this constructing process can be continued to get methods of arbitrary even order.展开更多
We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two-and three-dimensional spatial domains.In this method,waves are slowed down and dissipated in sponge layers near the ...We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two-and three-dimensional spatial domains.In this method,waves are slowed down and dissipated in sponge layers near the far-field boundaries.Mathematically,this is equivalent to a coordinate mapping that transforms a very large physical domain to a significantly smaller computational domain,where the elastic wave equation is solved numerically on a regular grid.To damp out waves that become poorly resolved because of the coordinate mapping,a high order artificial dissipation operator is added in layers near the boundaries of the computational domain.We prove by energy estimates that the super-grid modeling leads to a stable numerical method with decreasing energy,which is valid for heterogeneous material properties and a free surface boundary condition on one side of the domain.Our spatial discretization is based on a fourth order accurate finite difference method,which satisfies the principle of summation by parts.We show that the discrete energy estimate holds also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries.Therefore,the coefficients in the finite difference stencils need only be boundary modified near the free surface.This allows for improved computational efficiency and significant simplifications of the implementation of the proposed method in multi-dimensional domains.Numerical experiments in three space dimensions show that the modeling error from truncating the domain can be made very small by choosing a sufficiently wide super-grid damping layer.The numerical accuracy is first evaluated against analytical solutions of Lamb’s problem,where fourth order accuracy is observed with a sixth order artificial dissipation.We then use successive grid refinements to study the numerical accuracy in the more complicated motion due to a point moment tensor source in a regularized layered material.展开更多
文摘The suitability of six higher order root solvers is examined for solving the nonlinear equilibrium equations in large deformation analysis of structures.The applied methods have a better convergence rate than the quadratic Newton-Raphson method.These six methods do not require higher order derivatives to achieve a higher convergence rate.Six algorithms are developed to use the higher order methods in place of the Newton-Raphson method to solve the nonlinear equilibrium equations in geometrically nonlinear analysis of structures.The higher order methods are applied to both continuum and discrete problems(spherical shell and dome truss).The computational cost and the sensitivity of the higher order solution methods and the Newton-Raphson method with respect to the load increment size are comparatively investigated.The numerical results reveal that the higher order methods require a lower number of iterations that the Newton-Raphson method to converge.It is also shown that these methods are less sensitive to the variation of the load increment size.As it is indicated in numerical results,the average residual reduces in a lower number of iterations by the application of the higher order methods in the nonlinear analysis of structures.
文摘The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example problems from the fracture mechanics literature(with available analytical solutions) including center slant crack in an infinite and finite body, single and double edge cracks, cracks emanating from a circular hole. The numerical values of Mode Ⅰ and Mode Ⅱ SIFs for these problems using HODDM are in excellent agreement with analytical results(reaching up to 0.001% deviation from their analytical results). The HODDM is also compared with the XFEM and a modified XFEM results. The results show that the HODDM needs a considerably lower computational effort(with less than 400 nodes) than the XFEM and the modified XFEM(which needs more than 10000 nodes) to reach a much higher accuracy. The proposed HODDM offers higher accuracy and lower computation effort for a wide range of problems in LEFM.
基金financially supported by the National Natural Science Foundation of China (Grant Nos.52271276,52271319,and 52201364)the Natural Science Foundation of Jiangsu Province (Grant No.BK20201006)。
文摘A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.
文摘In this paper a framework for efficient irregular wave simulations using Higher Order Spectral method coupled with fully nonlinear viscous,two-phase Computational Fluid Dynamics(CFD)model is presented.CFD model is based on solution decomposition via Spectral Wave Explicit Navier-Stokes Equation method,allowing efficient coupling with arbitrary potential flow solutions.Higher Order Spectrum is a pseudo-spectral,potential flow method for solving nonlinear free surface boundary conditions up to an arbitrary order of nonlinearity.It is capable of efficient long time nonlinear propagation of arbitrary input wave spectra,which can be used to obtain realistic extreme waves.To facilitate the coupling strategy,Higher Order Spectrum method is implemented in foam-extend alongside the CFD model.Validation of the Higher Order Spectrum method is performed on three test cases including monochromatic and irregular wave fields.Additionally,the coupling between Higher Order Spectrum and CFD is validated on three hour irregular wave propagation.Finally,a simulation of a 3D extreme wave encountering a full scale container ship is shown.
文摘A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.
文摘The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid.The wavy shaped enclosure is equipped with onequarter of a conducting solid cylinder.The system of equations resulting from the mathematical modeling of the physical problem in its dimensionless form is discretized via the higher-order Galerkin-based finite element method(GFEM).The dependency of various factors and their interrelationships affecting the hydro-thermal behavior and heat exchange rate are delineated.The numerical experiments reveal that the best heat transfer rate is achieved for the pseudo-plastic hybrid nanoliquid with high Rayleigh number and thermal conductivity ratio and low Hartmann number.Besides,the power-law index has a major effect in deteriorating the heat convection at high Rayleigh number.
文摘In this paper, we develop a new technique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary differential equations. We call it a new method because we only see additive extrapolation method before. This new method has a great advantage over additive extrapolation method because it keeps group property. If this method is used to construct higher order schemes from lower symplectic schemes, the higher order ones are also symplectic. First we introduce the concept of adjoint methods and some of their properties. We show that there is a self-adjoint scheme corresponding to every method. With this self-adjoint scheme of lower order, we can construct higher order schemes by multiplicative extrapolation method, which can be used to construct even much higher order schemes. Obviously this constructing process can be continued to get methods of arbitrary even order.
基金the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.This is contribution LLNL-JRNL-610212.
文摘We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two-and three-dimensional spatial domains.In this method,waves are slowed down and dissipated in sponge layers near the far-field boundaries.Mathematically,this is equivalent to a coordinate mapping that transforms a very large physical domain to a significantly smaller computational domain,where the elastic wave equation is solved numerically on a regular grid.To damp out waves that become poorly resolved because of the coordinate mapping,a high order artificial dissipation operator is added in layers near the boundaries of the computational domain.We prove by energy estimates that the super-grid modeling leads to a stable numerical method with decreasing energy,which is valid for heterogeneous material properties and a free surface boundary condition on one side of the domain.Our spatial discretization is based on a fourth order accurate finite difference method,which satisfies the principle of summation by parts.We show that the discrete energy estimate holds also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries.Therefore,the coefficients in the finite difference stencils need only be boundary modified near the free surface.This allows for improved computational efficiency and significant simplifications of the implementation of the proposed method in multi-dimensional domains.Numerical experiments in three space dimensions show that the modeling error from truncating the domain can be made very small by choosing a sufficiently wide super-grid damping layer.The numerical accuracy is first evaluated against analytical solutions of Lamb’s problem,where fourth order accuracy is observed with a sixth order artificial dissipation.We then use successive grid refinements to study the numerical accuracy in the more complicated motion due to a point moment tensor source in a regularized layered material.
