The optimality criteria （OC） method and mathematical programming （MP） were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constrai...The optimality criteria （OC） method and mathematical programming （MP） were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constraints. The stress constraints as local constraints were approached by zero-order approximation and transformed into movable sectional lower limits with the full stress criterion. The displacement constraints as global constraints were transformed into explicit expressions with the unit virtual load method. Thus an approximate explicit model for the sectional optimization of frame structures was built with stress and displacement constraints. To improve the resolution efficiency, the dual-quadratic programming was adopted to transform the original optimization model into a dual problem according to the dual theory and solved iteratively in its dual space. A method called approximate scaling step was adopted to reduce computations and smooth the iterative process. Negative constraints were deleted to reduce the size of the optimization model. With MSC/Nastran software as structural solver and MSC/Patran software as developing platform, the sectional optimization software of frame structures was accomplished, considering stress and displacement constraints. The examples show that the efficiency and accuracy are improved.展开更多
This paper deals with the inertial manifold and the approximate inertialmanifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore,we provide the erro...This paper deals with the inertial manifold and the approximate inertialmanifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore,we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.展开更多
The three-dimensional problem involving diffraction of water wave by a finite floating rigid dock over an arbitrary bottom is studied for two cases(1)in the absence of wall(2)in the presence of wall.The problem is han...The three-dimensional problem involving diffraction of water wave by a finite floating rigid dock over an arbitrary bottom is studied for two cases(1)in the absence of wall(2)in the presence of wall.The problem is handled for its solution with the aid of step method.Here both asymmetric and symmetric arbitrary bottom profile is approximated using successive steps.Step approximation helps to apply the matched eigenfunction expansion method,in result,system of algebraic equations are obtained which are solved to determine the hydrodynamic quantities,namely,force experienced by rigid floating dock as well as rigid seawall,free surface elevation,transmission and reflection coefficients associated with transmission and reflected waves respectively.The effects of various structural and system parameters are examined on these hydrodynamics quantities.The appropriate values of length and thickness of dock,water depth and angle of incidence provide the salient information to marine and coastal engineers to design the offshore structures and creation of parabolic trench on the bottom.The present results are compared with known results in special case of bottom topography.The energy balance relation is derived and checked.展开更多
基金Project supported by the National Natural Science Foundation of China(No. 10472003) the Natural Science Foundation of Beijing(No.3002002) the Science Foundation of Beijing Municipal Commission of Education(No.KM200410005019)
文摘The optimality criteria （OC） method and mathematical programming （MP） were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constraints. The stress constraints as local constraints were approached by zero-order approximation and transformed into movable sectional lower limits with the full stress criterion. The displacement constraints as global constraints were transformed into explicit expressions with the unit virtual load method. Thus an approximate explicit model for the sectional optimization of frame structures was built with stress and displacement constraints. To improve the resolution efficiency, the dual-quadratic programming was adopted to transform the original optimization model into a dual problem according to the dual theory and solved iteratively in its dual space. A method called approximate scaling step was adopted to reduce computations and smooth the iterative process. Negative constraints were deleted to reduce the size of the optimization model. With MSC/Nastran software as structural solver and MSC/Patran software as developing platform, the sectional optimization software of frame structures was accomplished, considering stress and displacement constraints. The examples show that the efficiency and accuracy are improved.
文摘This paper deals with the inertial manifold and the approximate inertialmanifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore,we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.
文摘The three-dimensional problem involving diffraction of water wave by a finite floating rigid dock over an arbitrary bottom is studied for two cases(1)in the absence of wall(2)in the presence of wall.The problem is handled for its solution with the aid of step method.Here both asymmetric and symmetric arbitrary bottom profile is approximated using successive steps.Step approximation helps to apply the matched eigenfunction expansion method,in result,system of algebraic equations are obtained which are solved to determine the hydrodynamic quantities,namely,force experienced by rigid floating dock as well as rigid seawall,free surface elevation,transmission and reflection coefficients associated with transmission and reflected waves respectively.The effects of various structural and system parameters are examined on these hydrodynamics quantities.The appropriate values of length and thickness of dock,water depth and angle of incidence provide the salient information to marine and coastal engineers to design the offshore structures and creation of parabolic trench on the bottom.The present results are compared with known results in special case of bottom topography.The energy balance relation is derived and checked.
