A meshless algorithm with the improved moving least square approximation for nonlinear improved Boussinesq equation

An improved moving least square meshless method is developed for the numerical solution of the nonlinear improved Boussinesq equation. After the approximation of temporal derivatives, nonlinear systems of discrete algebraic equations are established and are solved by an iterative algorithm. Convergence of the iterative algorithm is discussed. Shifted and scaled basis functions are incorporated into the method to guarantee convergence and stability of numerical results. Numerical examples are presented to demonstrate the high convergence rate and high computational accuracy of the method.

Jackknife based generalized resampling reliability approach for rock slopes and tunnels stability analyses with limited data:Theory and applications

An efficient resampling reliability approach was developed to consider the effect of statistical uncertainties in input properties arising due to insufficient data when estimating the reliability of rock slopes and tunnels.This approach considers the effect of uncertainties in both distribution parameters(mean and standard deviation)and types of input properties.Further,the approach was generalized to make it capable of analyzing complex problems with explicit/implicit performance functions(PFs),single/multiple PFs,and correlated/non-correlated input properties.It couples resampling statistical tool,i.e.jackknife,with advanced reliability tools like Latin hypercube sampling(LHS),Sobol’s global sensitivity,moving least square-response surface method(MLS-RSM),and Nataf’s transformation.The developed approach was demonstrated for four cases encompassing different types.Results were compared with a recently developed bootstrap-based resampling reliability approach.The results show that the approach is accurate and significantly efficient compared with the bootstrap-based approach.The proposed approach reflects the effect of statistical uncertainties of input properties by estimating distributions/confidence intervals of reliability index/probability of failure(s)instead of their fixed-point estimates.Further,sufficiently accurate results were obtained by considering uncertainties in distribution parameters only and ignoring those in distribution types.

Three-Dimensional Meshfree Analysis of Interlocking Concrete Blocks for Step Seawall Structure

This study adapts the flexible characteristic of meshfree method in analyzing three-dimensional(3D)complex geometry structures,which are the interlocking concrete blocks of step seawall.The elastostatic behavior of the block is analysed by solving the Galerkin weak form formulation over local support domain.The 3D moving least square(MLS)approximation is applied to build the interpolation functions of unknowns.The pre-defined number of nodes in an integration domain ranging from 10 to 60 nodes is also investigated for their effect on the studied results.The accuracy and efficiency of the studied method on 3D elastostatic responses are validated through the comparison with the solutions of standard finite element method(FEM)using linear shape functions on tetrahedral elements and the well-known commercial software,ANSYS.The results show that elastostatic responses of studied concrete block obtained by meshfree method converge faster and are more accurate than those of standard FEM.The studied meshfree method is effective in the analysis of static responses of complex geometry structures.The amount of discretised nodes within the integration domain used in building MLS shape functions should be in the range from 30 to 60 nodes and should not be less than 20 nodes.

ICM Method Combined with Meshfree Approximation for Continuum Structure

The independent continuous mapping(ICM) method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented.To facilitate the enforcement of the essential boundary condition and derivative of various sensitivities,a singular weight function in element free Galerkin method is introduced.Material point variable is defined to illustrate the condition of material point and its vicinity instead of element or node.The topological variables field is constructed by moving least square approximation which inherits the continuity and smoothness of the weight function.Due to reciprocal relationships between the topological variables and design variables,various structural responses sensitivities are derived according to the method for calculating the partial derivatives of compound functions.Numerical examples indicate that checkerboard pattern and mesh-dependence phenomena are overcome without additional restriction methods.

Reliability assessment of deep excavations in spatially random cohesion weakening friction strengthening massive rocks:Application to nuclear repositories

An augmented methodology is developed to estimate the reliability of deep excavations along spatially variable massive rock masses using the cohesion weakening friction strengthening(CWFS)model.Sensitive parameters of the CWFS model were initially identified using Sobol’s global sensitivity analysis based on their influence on the displacements and excavation damage zone around excavations.The probability of failure was estimated by performing Mont–Carlo Simulations on random finite difference models of excavations generated via MATLAB-FLAC2D coupling,considering the spatial variation of these sensitive parameters.Spatial variation was modeled by generating anisotropic random fields of sensitive CWFS parameters via the recently developed Fourier series method and updated correlations suggested by Walton(2019).The proposed methodology was demonstrated for a proposed deep nuclear waste repository to be located in Canada.Results from the developed methodology were systematically compared with those of traditional reliability(ignoring spatial variation)and deterministic methods(ignoring uncertainty).Although the developed methodology was computationally complex,it was judged to be the most realistic due to the realistic consideration of heterogeneous distributions of rock properties.Traditional methodologies underestimate/overestimate the excavation performance due to negligence of uncertainty and spatial variability.Finally,a parametric analysis was performed using developed methodology by varying the initial friction angle,scale of fluctuations(SOFs)and dilation angle.The effect of initial friction angle was observed to be more pronounced on the probability of failures as compared to SOFs and dilation angle.Similar observations were made related to the excavation damage zone(EDZ)development quantified using yield area ratio.