Fretting fatigue behavior of Ni-base single crystal(NBSX) superalloys was investigated based on crystal plasticity finite element method(CPFEM) simulation. Crystal plasticity constitutive model considering cyclic hard...
详细信息
Fretting fatigue behavior of Ni-base single crystal(NBSX) superalloys was investigated based on crystal plasticity finite element method(CPFEM) simulation. Crystal plasticity constitutive model considering cyclic hardening effect was employed. CPFEM simulation showed the activations of crystallographic slip systems at contact region. The slip plane with the maximum plastic slip was determined as dominate slip plane. Equivalent plastic strain was proved effective to predict crack initiation. The simulation results including predicted slip lines, crack initiation locations and orientations were in good agreements with observations.
In this paper, the Element Differential Method(EDM) is coupled with the Multi-Domain Boundary Element Method(MDBEM) for solving general multi-scale heat conduction and mechanical problems. The basic algebraic equation...
详细信息
In this paper, the Element Differential Method(EDM) is coupled with the Multi-Domain Boundary Element Method(MDBEM) for solving general multi-scale heat conduction and mechanical problems. The basic algebraic equations in BEM are formulated in terms of displacements/temperatures and tractions/fluxes, which are the same as those in EDM. So when coupling these two methods, we don't need to transform the variables like the equivalent nodal force into the surface traction as done in the finite element method(FEM). The key task in the proposed coupling method is to use the displacement consistency condition and the traction equilibrium equation at interface nodes of two methods to eliminate all BEM nodes except for those on the interfaces. The detailed elimination process is presented in this paper, which can result in the final system of equations without iteration. The coefficient matrix of the final coupled system is sparse even though a small part is dense. The coupling method inherits the advantage of EDM in flexibility and computational efficiency, and the advantage of BEM in the robustness of treating multi-scale problems. A number of numerical examples of general heat conduction and mechanical problems are given to demonstrate the correctness and efficiency of this coupling method.
This work aims at improving the acoustic performance of system using optimization technique, where the boundary element method(BEM) is employed for acoustic/vibro-acoustic analysis. Our work consists of two main parts...
详细信息
This work aims at improving the acoustic performance of system using optimization technique, where the boundary element method(BEM) is employed for acoustic/vibro-acoustic analysis. Our work consists of two main parts. In part I, we perform shape optimization for sound scattering problems via isogeometric analysis(IGA), where IGA provides exact geometric representations. Furthermore, refinements and shape changes for the design model are easily implemented without mesh regeneration, which significantly reduces subsequent communication with the original description. In this part, the fast sensitivity analysis approach based on the fast multipole method(FMM) and direct diff erentiation method(DDM) are developed to calculate the sensitivities of objective function with respect to design variables. In part II, the topology optimization is performed by setting the artificial element densities of porous material or structural domain as design variable. Regarding the optimization of porous material, the admittance boundary conditions are included into the BEM. For the topology optimization of the structural domain, the coupled finite element method/boundary element method scheme is used for the system response analysis, where the strong interaction between the structural domain and acoustic domain is considered. Different from the shape optimization, the adjoint variable method(AVM) is preferred due to the large number of design variables for the topology optimization. The FMM is also applied to accelerate the adjoint sensitivity analysis to improve overall computational efficiency. After the acoustic state and sensitivity information are obtained, the method of moving asymptotes(MMA) is used for solving the optimization problem to find the optimal solution. We validate the proposed optimization procedure through a number of numerical simulations.
This talk explores the tradeoffs between the strong and weak formulation for solving partial differential equations. Finite element method is based on weak formulation, which requires integration over the domain. In o...
详细信息
This talk explores the tradeoffs between the strong and weak formulation for solving partial differential equations. Finite element method is based on weak formulation, which requires integration over the domain. In order to perform the integration, the domain is divided into regular shaped elements. For the purpose of integration, low degree polynomials are used for interpolation. Due to the discontinuity between the elements, its error convergence can only be algebraic, such as hn, where h is the element size, and n is typically 2 or 3. Collocation method is a much older method, and is based on strong formulation. The solution is approximated by a series using certain basis function, with unknown coefficients. The approximate solution is required to satisfy the governing equation or boundary conditions at a set of nodes, with its number equals to the number of unknowns in the series. These methods use global interpolation and often have exponential error convergence, exp(-1/h), such as Chebyshev and Fourier spectral methods. These methods however require a regular(rectangular) domain;hence are rarely used in applications. The situation changed when the radial basis function(RBF) was introduced with theoretical support three decades ago. RBF collocation allows the use of scattered points to fit arbitrary geometry and has exponential convergence. The global interpolation, however, creates a full matrix with high condition number, which can prohibit a large number of nodes to be used. In the last two decades, FEM sees its deficiency with elements, and started to eliminate them, to become meshless(element-free). It however retains the weak formulation. In the last decades, RBF collocation started to use local interpolation, with reduced matrix condition number, but sacrificed accuracy. Even finite difference method started to abandon the rectilinear grid by using scattered points. It seems that all methods start to converge by using scattered points and local interpol
暂无评论