Mesh deformation technique is widely used in many application fields, and has received a lot of attentions in recent years. This paper focuses on the methodology and algorithm of algebraic type mesh deformation for unstructured mesh in numerical discretization. To preserve mesh quality effectively, an algebraic approach for two and three dimensional unstructured mesh is developed based on mean value coordinates interpolation combined with node visibility analysis.The proposed approach firstly performs node visibility analysis to find out the visible boundary for each grid point to be moved, then evaluates the mean value coordinates of each grid point with respect to all vertices on its visible boundary. Thus the displacements of grid points can be calculated by interpolating the boundary movement by the mean value coordinates. Compared with other methods, the proposed method has good deformation capability and predictable computational cost, with no need to select parameters or functions. Applications of mesh deformation in different fields are presented to demonstrate the effectiveness of the proposed approach. The results of numerical experiments exhibit not only superior deformation capability of the method in traditional applications of fluid dynamic grid, but also great potential in modeling for large deformation analysis and inverse design problems.
By taking the frozen soil as a particle-reinforced composite material which consists of clay soil(i.e., the matrix) and ice particles, a micromechanical constitutive model is established to describe the dynamic compressive deformation of frozen soil. The proposed model is constructed by referring to the debonding damage theory of composite materials, and addresses the effects of strain rate and temperature on the dynamic compressive deformation of frozen soil. The proposed model is verified through comparison of the predictions with the corresponding dynamic experimental data of frozen soil obtained from the split Hopkinson pressure bar(SHPB) tests at different high strain rates and temperatures. It is shown that the predictions agree well with the experimental results.
A simple experimental method was introduced to study the mechanical properties of reinforced concrete under shock loading. The one-stage light gas gun was used to test the mechanical properties of reinforced concrete with different reinforcement ratios under various impact velocities. Three Mn-Cu piezoresistive pressure gauges embedded in the target were used to record the voltage-time signals, from which the stress-strain curves of reinforced concrete were obtained using Lagrangian analysis. Experimental results indicated that the load-bearing capacities of reinforced concrete increased greatly with the impact velocity and the reinforcement ratio. The peak stress of the shock wave decreased exponentially with the propagation distance.
Reliability and optimization are two key elements for structural design. The reliabilitybased topology optimization(RBTO) is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topology optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach(the performance measure approach, PMA) and the decoupled approaches(the so-called Hybrid method and the sequential optimization and reliability assessment, SORA). For reliability analysis, the stochastic response surface method(SRSM) was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique.The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the deterministic, RBTOs were compared with one another; and useful conclusions regarding validity,accuracy and efficiency were drawn.
An analytical solution is obtained for the Functionally Graded Shape Memory Alloy(FG-SMA) composites subjected to thermo-mechanical coupling. Young’s modulus and thermal expansion coefficient of the material are assumed to vary in different forms of power function through the thickness, with the Poisson’s ratio being constant. An SMA constitutive model is combined with the averaging techniques of composite to determine the mechanical properties of the FG-SMA composites. Different phase transformation steps and the corresponding stress distributions through the thickness direction are given. The results show that the average stresses decrease as the transformations proceed.
Novel micromechanical curved beam models were presented for predicting the tensile and shear moduli of triaxial weave fabric(TWF) composites by considering the interactions between the triaxial yarns of 0?and±60?. The triaxial yarns in micromechanical representative unit cell(RUC) were idealized as curved beams with a path depicted using the sinusoidal shape functions, and the tensile and shear moduli of TWF composites were derived by means of the strain energy approach founded on micromechanics. In order to validate the new models, the predictions were compared with the experimental data from literature. It was shown that the predictions from the new model agree well with the experimental results. Using these models, the tensile and shear properties of TWF composites could be predicted based only on the properties of basic woven fabric.
A Discrete Element Method(DEM) model is developed to study the particle breakage effect on the one-dimensional compression behavior of silica sands. The ‘maximum tensile stress’ breakage criterion considering multiple contacts is adopted to simulate the crushing of circular particles in the DEM. The model is compared with published experimental results. Comparison between the compression curves obtained from the numerical and experimental results shows that the proposed method is very effective in studying the compression behavior of silica sands considering particle breakage. The evolution of compression curves at different stress levels is extensively studied using contact force distribution, variation of contact number and particle size distribution curve with loading. It is found that particle breakage has great impact on compression behavior of sand, particularly after the yield stress is reached and particle breakage starts.The crushing probability of particles is found to be macroscopically affected by stress level and particle size distribution curve, and microscopically related to the evolutions of contact force and coordination number. Once the soil becomes well-graded and the average coordination number is greater than 4 in two-dimension, the crushing probability of parent particles can reduce by up to5/6. It is found that the average contact force does not always increase with loading, but increases to a peak value then decreases once the soil becomes more well-graded. It is found through the loading rate sensitivity analysis that the compression behavior of sand samples in the DEM is also affected by the loading rate. Higher yield stresses are obtained at higher loading rates.