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| 1 | Meshless Methods Coupled with Other Numerical Methods显示文摘Meshless or mesh-free (or shorten as MFree) methods have been proposed and achieved remarkable progress over the past few years. The idea of combining MFree methods with other existing numerical techniques such as the finite element method (FEM) and the boundary element method (BEM), is naturally of great interest in many practical applications. However, the shape functions used in some MFree methods do not have the Kronecker delta function property. In order to satisfy the combined conditions of displacement compatibility, two numerical techniques, using the hybrid displacement shape function and the modified variational form, are developed and discussed in this paper. In the first technique, the original MFree shape functions are modified to the hybrid forms that possess the Kronecker delta function property. In the second technique, the displacement compatibility is satisfied via a modified variational form based on the Lagrange multiplier method. Formulations of several coupled methods are presented. Numerical exam- ples are presented to demonstrate the effectiveness of the present coupling methods. | Y.T.GU G.R.LIU | 2005 | Tsinghua Science and Technology2005，10，1： | 9 |
| 2 | A node-based smoothed point interpolation method for dynamic analysis of rotating flexible beams显示文摘We proposed a mesh-free method, the called node-based smoothed point interpolation method(NS-PIM),for dynamic analysis of rotating beams. A gradient smoothing technique is used, and the requirements on the consistence of the displacement functions are further weakened. In static problems, the beams with three types of boundary conditions are analyzed, and the results are compared with the exact solution, which shows the effectiveness of this method and can provide an upper bound solution for the deflection.This means that the NS-PIM makes the system soften. The NS-PIM is then further extended for solving a rigid-flexible coupled system dynamics problem, considering a rotating flexible cantilever beam. In this case, the rotating flexible cantilever beam considers not only the transverse deformations,but also the longitudinal deformations. The rigid-flexible coupled dynamic equations of the system are derived via employing Lagrange's equations of the second type. Simulation results of the NS-PIM are compared with those obtained using finite element method(FEM) and assumed mode method. It is found that compared with FEM, the NS-PIM has anti-ill solving ability under the same calculation conditions. | C.F.Du D.G.Zhang L.Li G.R.Liu | 2018 | Acta Mechanica Sinica2018，34，2： | 3 |
| 3 | 查看详情显示文摘 | C.E.Zhou G.R.Liu K.Y.Lou | | 0，，： | 1 |
| 4 | Real-time prediction of projectile penetration to laminates by training machine learning models with finite element solver as the trainer显示文摘Studies on ballistic penetration to laminates is complicated,but important for design effective protection of structures.Experimental means of study is expensive and can often be dangerous.Numerical simulation has been an excellent supplement,but the computation is time-consuming.Main aim of this thesis was to develop and test an effective tool for real-time prediction of projectile penetrations to laminates by training a neural network and a decision tree regression model.A large number of finite element models were developed;the residual velocities of projectiles from finite element simulations were used as the target data and processed to produce sufficient number of training samples.Study focused on steel 4340tpolyurea laminates with various configurations.Four different 3D shapes of the projectiles were modeled and used in the training.The trained neural network and decision tree model was tested using independently generated test samples using finite element models.The predicted projectile velocity values using the trained machine learning models are then compared with the finite element simulation to verify the effectiveness of the models.Additionally,both models were trained using a published experimental data of projectile impacts to predict residual velocity of projectiles for the unseen samples.Performance of both the models was evaluated and compared.Models trained with Finite element simulation data samples were found capable to give more accurate predication,compared to the models trained with experimental data,because finite element modeling can generate much larger training set,and thus finite element solvers can serve as an excellent teacher.This study also showed that neural network model performs better with small experimental dataset compared to decision tree regression model. | Pushkar Wadagbalkar G.R.Liu | 2021 | Defence Technology(防务技术)2021，17，1： | 0 |
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