Multiresolution method for bending of plates with complex shapes

A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.

Mechanical analysis of interaction between plant roots and rock and soil mass in slope vegetation

With the help of plant roots, slope vegetation makes the slope soil mass be-come a composite material of soil and roots, and thus enhances shear strength of the slope soil mass and stability of the slope. However, the related studies at present are still qualitative. In this paper, quantitative analysis of the interaction between roots and soil mass are made. By the analysis of the interaction between herbaceous plant roots including lateral roots of woody plants and rock and soil mass, a mechanical model of the interaction between frictional roots and soil is established, and its correctness is shown. A mechanical model of the interaction between anchorage root, namely, woody plant taproot, and soil is also established. The establishment of the models provides a useful means in quantitative analysis of the interaction between plant roots and soil, and has practical values.

Effect of salts on earthen materials deterioration after humidity cycling

Salt weathering leads to destruction of many valuable cultural heritage monuments and porous building material. The present study aims at providing more laboratory evidence for evaluating the effects of salt precipitation on the deterioration process. In view of this, the remoulded soil specimens were mixed with three kinds of salts(i.e., NaCl, Na_2SO_4 and their mixture) with different salt concentrations, and the specimens were kept in environment cabinet for undergoing different wet-dry cycles. After each cycle, the ultrasound velocity measurements were employed to monitor the deterioration process. For the specimens that have suffered three wet-dry cycles, the mechanical properties(i.e. shear strength and compression strength) were determined to evaluate the degree of deterioration. Furthermore, considering the realistic conservation environment of earthen sites, mechanical stability of these specimens against sediment-carrying wind erosion was conducted in a wind tunnel. These experiments results indicate that the overall average velocities of the specimens after the third cycle are significantly lower than those subjected to only one cycle. Ultrasound velocity, mechanical strength and wind erosion rate decrease when salt content increases. However, the internal friction angle increases firstly, and then decreases with the increase in salt content added to the specimens. Na_2SO_4 contributes most of the surface deterioration, while NaCl plays little role in the deterioration. The damage potential of the salt mixture is less obvious and largely dependent on the crystallisation location.

Effect of drying cracks on swelling and self-healing of bentonite-sand blocks used as engineered barriers for radioactive waste disposal

Experiments were conducted to evaluate the healing of drying cracks in air-dried bentonite-sand blocks after hydration and swelling in groundwater,providing justifications to simplify the protection of blocks prior to installation in a high-level radioactive waste repository.Synthetic groundwater was prepared to represent the geochemistry of Beishan groundwater,and was used to hydrate the blocks during the swelling pressure and swelling strain measurements,as Beishan is the most promising site for China's repository.Healing of the surface cracks was recorded by photography,and healing of the internal cracks was visualized by CT images and hydraulic conductivity of air-dried blocks.The results indicate that the maximum swelling pressure and swelling strain are primarily affected by the geochemistry of Beishan groundwater,but not affected by the drying cracks.The maximum swelling pressure and swelling strain of air-dried blocks are comparable to or even higher than the pressure and strain of fresh blocks.The maximum swelling pressure measured in strong(i.e.high ion strength)Beishan groundwater was 44%of the pressure measured in deionized(DI)water,and the maximum swelling strain was reduced to 23%of the strain measured in DI water.Nevertheless,the remained swelling of the blocks hydrated in strong Beishan groundwater was sufficient to heal the surface and internal drying cracks,as demonstrated by the pictures of surface cracks and CT images.The hydraulic conductivity of the air-dried block permeated with strong groundwater was comparable(3.7×higher)to the hydraulic conductivity of the fresh block,indicating the self-healing of drying cracks after hydration and swelling in groundwater.A simplified method of protecting the block with plastic wraps before installation is recommended,since the remained swelling of the block hydrated in Beishan groundwater is sufficient to heal the drying cracks.

Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix.The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities,including transcendental ones,in which the discretization process is as simple as that in solving linear problems,and only common two-term connection coefficients are needed.All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method,which does not require numerical integration in the resulting nonlinear discrete system.The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers.The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids,and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids.In addition,Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method,including the initial guess far from real solutions.

Mechanical interaction between roots and soil mass in slope vegetation

The most basic function of slope vegetation is to strengthen rock and soil mass through plant roots which increase the shear strength of the slope markedly and thereby increase the stability of the slope. However, the calculation of the reinforcement ability of slope vegetation still remains at the stage of judging by experience, because it is rather difficult due to the intricacy and volatility of the force condition of plant roots in rock and soil medium. Although some scholars have tried to study the interaction between plant roots and soil mass, the systemic analysis of the mechanical reinforcement mechanism and the contribution of plant roots to strengthening the rock and soil mass on the surface of the slope is untapped. In this paper, by analyzing the mechanism of slope vegetation and the corresponding reinforcement effect, the effects that slope vegetation generates on the shear strength of slope soil mass are studied, thereby a theoretical basis for plant protection designing is provided.

Three-dimensional meta-architecture with programmable mechanical properties

Artificial metamaterials have attracted widespread attention of research communities due to their anomalous physical properties compared to those of conventional materials.In this study,we designed a three-dimensional(3D)lightweight metaarchitecture consisting of 6-connected anti-chiral honeycombs.The mechanical properties(e.g.Young’s modulus,compression strength,and Poisson’s ratio)of the proposed meta-architecture could be programmed by adjusting a series of geometric parameters,as shown through numerical simulations.Moreover,an optically sensitive polymer-based 3D meta-architecture with 6-connected anti-chiral features was constructed by the stereolithography method.Owing to the regulation of the negative Poisson’s ratio,3D meta-architecture achieved a greater ductility under compression than those of traditional truss structures while retaining a relatively high strength and low density.Compression experiments validated the excellent tunability of the mechanical properties of the proposed 3D 6-connected antichiral structure.The results suggest the promising applications of this structure in lightweight aircraft,vibration isolation,and mechanical sensors.