Some Ideas and Progress on the Shape Optimization of Nonlinear Structures

AbstractFor the sensitivity analysis of nonlinear structure with respect to the shape variation, it is formulated based on the geometrical mapping approach, rather than the material derivative approach. The shape variation is regarded as a mapping characterized by the shape variation velocity field, or a fictitious deformation of the continuum, which is not real displacement, and there are no strain and stress corresponding to such fictitious displacement field. Started from the virtual work principle, the sensitivity equations of state variables for nonlinear structure with respect to the shape variation have been formulated, and also the equation for calculating the sensitivity of performances with respect to the shape variation. To enhance the efficiency, the adjoint variable method is applied, wherein the asymmetry of the equation matrix due to the slip contacted case of the frictional contact using Lagrange multiplier method is taken into account. For the gradient-based Kriging method based on the samples determined by the orthogonal maximin Latin hypercube design, a criterion for the best likelihood spatial correlation parameter is suggested, based on the transition from insufficient to excessive control. The criterion is verified using a series of test examples

BINN: A deep learning approach for computational mechanics problems based on boundary integral equations

We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are approximated using neural networks and solved through a training process. The loss function is chosen as the residuals of the boundary integral equations. Regularization techniques are adopted to efficiently evaluate the weakly singular and Cauchy principle integrals in boundary integral equations. Potential problems and elastostatic problems are mainly concerned in this article as a demonstration. The proposed method has several outstanding advantages: First, the dimensions of the original problem are reduced by one, thus the freedoms are greatly reduced. Second, the proposed method does not require any extra treatment to introduce the boundary conditions, since they are naturally considered through the boundary integral equations. Therefore, the method is suitable for complex geometries. Third, BINN is suitable for problems on the infinite or semi-infinite domains. Moreover, BINN can easily handle heterogeneous problems with a single neural network without domain decomposition

Some Aspects of the BEM Research in China

In this paper, a short historical review of the BEM research in China is given first. The investigation on the BEM in China was started in 1978 at the Tsinghua University, based on the pioneering work published by Frank Rizzo [F. J. Rizzo, An integral equation approach to boundary value problems of classical elastostatics, Quart. Appl. Math., 25, 83-95 (1967)] and others. During the last 25 years, we have organized six national conferences on BEM, two international conferences and eight China-Japan/Japan-China symposia on BEM. The BEM investigations in the authors’ group at Tsinghua are briefly introduced next. Some representative investigations by other groups in Mainland China are also introduced. The related papers and other publications are listed in the References

Simulation of 2D Elastic Bodies with Randomly Distributed Circular Inclusions Using the BEM

Based on the Rizzo’s direct boundary integral equation formulation for elasticity problems, elastic bodies with randomly distributed circular inclusions are simulated using the boundary element method. The given numerical examples show that the boundary element method is more accurate and more efficient than the finite element method for such type of problems. The presented approach can be successfully applied to estimate the equivalent elastic properties of many composite materials

Ringelemente fuer elastische Rotationsschalen unter instationaerer thermischer Beanspruchung

Available from Bochum Univ. (DE). Inst. fuer Konstruktiven Ingenieurbau / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Numerical Simulation of the Enrichment of Chemotactic Bacteria in Oil-Water Two-Phase Transfer Fields of Heterogeneous Porous Media

Oil pollution in soil-groundwater systems is difficult to remove, and a large amount of residual oil is trapped in the low permeable layer of the heterogeneous aquifer. Aromatic hydrocarbons in oil have high toxicity and low solubility in water, which are harmful to the ecological environment. Chemotactic degrading bacteria can perceive the concentration gradient of non-aqueous phase liquid (NAPL) pollutants in the groundwater environment, and enrich and proliferate around the pollutants, thus achieving a more efficient and thorough remediation effect. However, the existing theoretical models are relatively simple. The physical fields of oil–water two-phase flow and oil-phase solute convection and diffusion in water are not coupled, which further restricts the accuracy of studies on bacterial chemotaxis to NAPL. In this study, geometric models based on the actual microfluidic experimental study were constructed. Based on the phase field model, diffusion convection equation and chemotaxis velocity equation, the effects of heterogeneity of porous media, wall wettability and groundwater flow rate on the residual oil and the concentration distribution of chemotaxis bacteria were studied. Under all of the simulation conditions, the residual oil in the high permeable area was significantly lower than that in the low permeable area, and the wall hydrophilicity enhanced the water flooding effect. Chemotactic bacteria could react to the concentration gradient of pollutants dissolved into water in the oil phase, and enrich near the oil–water interface with high concentration of NAPL, and the density of chemotactic bacteria at the oil–water interface can be up to 1.8–2 times higher than that in the water phase at flow rates from 1.13 to 6.78 m/d

Low-Frequency Acoustic-Structure Analysis Using Coupled FEM-BEM Method

A numerical algorithm based on finite element method (FEM) and boundary element method (BEM) is proposed for the analyses of acoustic-structure coupled problems. By this algorithm, the structural domain and the acoustic domain are modelled by FEM and BEM, respectively, which are coupled with each other through the consideration of the appropriate compatibility and equilibrium conditions on the interface of the two domains. To improve the computational efficiency, the adaptive cross approximation (ACA) approach is incorporated into the proposed algorithm to deal with the nonsymmetric and fully populated matrices resulting from the coupling of the FEM and BEM. The validity and the high efficiency of the present approach are demonstrated by two examples