We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space.The model describes the motion of the film/...We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space.The model describes the motion of the film/vapor interface with contact line migration and is governed by the surface diffusion equation with proper boundary conditions at the contact line.We present a weak formulation for the problem,in which the contact angle condition is weakly enforced.By using piecewise linear elements in space and backward Euler method in time,we then discretize the formulation to obtain a parametric finite element approximation,where the interface and its contact line are evolved simultaneously.The resulting numerical method is shown to be well-posed and unconditionally energystable.Furthermore,the numerical method is generalized to the case of anisotropic surface energies in the Riemannian metric form.Numerical results are reported to show the convergence and efficiency of the proposed numerical method as well as the anisotropic effects on the morphological evolution of thin films in solid-state dewetting.展开更多
The shape and size optimization of brackets in hull structures was conducted to achieve the simultaneous reduction of mass and high stress,where the parametric finite element model was built based on Patran Command La...The shape and size optimization of brackets in hull structures was conducted to achieve the simultaneous reduction of mass and high stress,where the parametric finite element model was built based on Patran Command Language codes.The optimization procedure was executed on Isight platform,on which the linear dimensionless method was introduced to establish the weighted multi-objective function.The extreme processing method was applied and proved effective to normalize the objectives.The bracket was optimized under the typical single loads and design waves,accompanied by the different proportions of weights in the objective function,in which the safety factor function was further established,including yielding,buckling,and fatigue strength,and the weight minimization and safety maximization of the bracket were obtained.The findings of this study illustrate that the dimensionless objectives share equal contributions to the multi-objective function,which enhances the role of weights in the optimization.展开更多
An efficient reliability-based design optimization method for the support structures of monopile offshore wind turbines is proposed herein.First,parametric finite element analysis(FEA)models of the support structure a...An efficient reliability-based design optimization method for the support structures of monopile offshore wind turbines is proposed herein.First,parametric finite element analysis(FEA)models of the support structure are established by considering stochastic variables.Subsequently,a surrogate model is constructed using a radial basis function(RBF)neural network to replace the time-consuming FEA.The uncertainties of loads,material properties,key sizes of structural components,and soil properties are considered.The uncertainty of soil properties is characterized by the variabilities of the unit weight,friction angle,and elastic modulus of soil.Structure reliability is determined via Monte Carlo simulation,and five limit states are considered,i.e.,structural stresses,tower top displacements,mudline rotation,buckling,and natural frequency.Based on the RBF surrogate model and particle swarm optimization algorithm,an optimal design is established to minimize the volume.Results show that the proposed method can yield an optimal design that satisfies the target reliability and that the constructed RBF surrogate model significantly improves the optimization efficiency.Furthermore,the uncertainty of soil parameters significantly affects the optimization results,and increasing the monopile diameter is a cost-effective approach to cope with the uncertainty of soil parameters.展开更多
基金supported by Singapore MOE grant MOE2019-T2-1-063(R-146-000-296-112)supported by the Singapore MOE grant R-146-000-285-114.
文摘We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space.The model describes the motion of the film/vapor interface with contact line migration and is governed by the surface diffusion equation with proper boundary conditions at the contact line.We present a weak formulation for the problem,in which the contact angle condition is weakly enforced.By using piecewise linear elements in space and backward Euler method in time,we then discretize the formulation to obtain a parametric finite element approximation,where the interface and its contact line are evolved simultaneously.The resulting numerical method is shown to be well-posed and unconditionally energystable.Furthermore,the numerical method is generalized to the case of anisotropic surface energies in the Riemannian metric form.Numerical results are reported to show the convergence and efficiency of the proposed numerical method as well as the anisotropic effects on the morphological evolution of thin films in solid-state dewetting.
基金This work was financially supported by the Key Research and Development Project of Shandong Province(Grant No.2020CXGC010702).
文摘The shape and size optimization of brackets in hull structures was conducted to achieve the simultaneous reduction of mass and high stress,where the parametric finite element model was built based on Patran Command Language codes.The optimization procedure was executed on Isight platform,on which the linear dimensionless method was introduced to establish the weighted multi-objective function.The extreme processing method was applied and proved effective to normalize the objectives.The bracket was optimized under the typical single loads and design waves,accompanied by the different proportions of weights in the objective function,in which the safety factor function was further established,including yielding,buckling,and fatigue strength,and the weight minimization and safety maximization of the bracket were obtained.The findings of this study illustrate that the dimensionless objectives share equal contributions to the multi-objective function,which enhances the role of weights in the optimization.
基金supported by the National Natural Science Foundation of China(Grant No.12072104)the National Key R&D Program of China(No.2018YFC0406703)。
文摘An efficient reliability-based design optimization method for the support structures of monopile offshore wind turbines is proposed herein.First,parametric finite element analysis(FEA)models of the support structure are established by considering stochastic variables.Subsequently,a surrogate model is constructed using a radial basis function(RBF)neural network to replace the time-consuming FEA.The uncertainties of loads,material properties,key sizes of structural components,and soil properties are considered.The uncertainty of soil properties is characterized by the variabilities of the unit weight,friction angle,and elastic modulus of soil.Structure reliability is determined via Monte Carlo simulation,and five limit states are considered,i.e.,structural stresses,tower top displacements,mudline rotation,buckling,and natural frequency.Based on the RBF surrogate model and particle swarm optimization algorithm,an optimal design is established to minimize the volume.Results show that the proposed method can yield an optimal design that satisfies the target reliability and that the constructed RBF surrogate model significantly improves the optimization efficiency.Furthermore,the uncertainty of soil parameters significantly affects the optimization results,and increasing the monopile diameter is a cost-effective approach to cope with the uncertainty of soil parameters.
