Modeling elastic wave propagation in fluid-filled boreholes drilled in nonhomogeneous media: BEM – MLPG versus BEM-FEM coupling

The efficiency of two coupling formulations, the boundary element method (BEM)-meshless local Petrov–Galerkin (MLPG) versus the BEM-finite element method (FEM), used to simulate the elastic wave propagation in fluid-filled boreholes generated by a blast load, is compared. The longitudinal geometry is assumed to be invariant in the axial direction (2.5D formulation). The material properties in the vicinity of the borehole are assumed to be nonhomogeneous as a result of the construction process and the ageing of the material. In both models, the BEM is used to tackle the propagation within the fluid domain inside the borehole and the unbounded homogeneous domain. The MLPG and the FEM are used to simulate the confined, damaged, nonhomogeneous, surrounding borehole, thus utilizing the advantages of these methods in modeling nonhomogeneous bounded media. In both numerical techniques the coupling is accomplished directly at the nodal points located at the common interfaces. Continuity of stresses and displacements is imposed at the solid–solid interface, while continuity of normal stresses and displacements and null shear stress are prescribed at the fluid–solid interface. The performance of each coupled BEM-MLPG and BEM-FEM approach is determined using referenced results provided by an analytical solution developed for a circular multi-layered subdomain. The comparison of the coupled techniques is evaluated for different excitation frequencies, axial wavenumbers and degrees of freedom (nodal points).Ministerio de Economía y Competitividad BIA2013-43085-PCentro Informático Científico de Andalucía (CICA

Finite Block Method and Applications in Engineering with Functional Graded Materials

PhDFracture mechanics plays an important role in understanding the performance of all types of materials including Functionally Graded Materials (FGMs). Recently, FGMs have attracted the attention of various scholars and engineers around the world since its specific material properties can smoothly vary along the geometries. In this thesis, the Finite Block Method (FBM), based on a 1D differential matrix derived from the Lagrangian Interpolation Method, has been presented for the evaluation of the mechanical properties of FGMs on both static and dynamic analysis. Additionally, the coefficient differential matrix can be determined by a normalized local domain, such as a square for 2D, a cubic for 3D. By introducing the mapping technique, a complex real domain can be divided into several blocks, and each block is possible to transform from Cartesian coordinate (xyz) to normalized coordinate ( ) with 8 seeds for two dimensions and 20 seeds for three dimensions. With the aid of coefficient differential matrix, the differential equation is possible to convert to a series of algebraic functions. The accuracy and convergence have been approved by comparison with other numerical methods or analytical results. Besides, the stress intensity factor and T-stresses are introduced to assess the fracture characteristics of FGMs. The Crack Opening displacement is applied for the calculation of the stress intensity factor with the FBM. In addition, a singular core is adopted to combine with the blocks for the simulation of T stresses. Numerical examples are introduced to verify the accuracy of the FBM, by comparing with Finite Element Methods or analytical results. Finally, the FBM is applied for wave propagation problems in two- and three-dimensional porous mediums considering their poroelasticities. To demonstrate the accuracy of the present method, a one-dimensional analytical solution has been derived for comparison

Meshless Investigation for Nonlocal Elasticity: Static and Dynamic

PhDThe numerical treatment of nonlocal problems, which taking into account material microstructures, by means of meshless approaches is promising due to its efficiency in addressing integropartial differential equations. This thesis focuses on the investigation of meshless methods to nonlocal elasticity. Firstly, mathematical constructions of meshless shape functions are introduced and their properties are discussed. Shape functions based upon different radial basis function (RBF) approximations are implemented and solutions are compared. Interpolation errors of different meshless shape functions are examined. Secondly, the Point Collocation Method (PCM), which is a strong-form meshless method, and the Local Integral Equation Method (LIEM) that bases on the weak-form, are presented. RBF approximations are employed both in PCM and LIEM. The influences of support domains, different kinds of RBFs and free parameters are studied in PCM. While in LIEM, analytical forms of integrals, which is new in meshless method, is addressed. And, the number of straight lines that enclose the local integral domain as well as the integral radius are analyzed. Several examples are conducted to demonstrate the accuracy of PCM and LIEM. Besides, comparisons are made with Abaqus solutions. Then, PCM and LIEM are applied to nonlocal elastostatics based on the Eringen’s model. Formulations of both methods are reported in the nonlocal frame. Numerical examples are presented and comparisons between solutions obtained from both methods are made, validating the accuracy and effectiveness of meshless methods for solving static nonlocal problems. Simultaneously, the influence of characteristic length and portion factors are investigated. Finally, LIEM is employed to solve nonlocal elastodynamic problems. The Laplace transform method and the time-domain technique are implemented in LIEM respectively as the time marching schemes. Numerical solutions of both approaches are compared, showing reasonable agreements. The influence of characteristic length and portion factors are investigated in nonlocal dynamic cases as well.China Scholarship Counci

The Finite Block Method: A Meshless Study of Interface Cracks in Bi-Materials

PhDThe ability to extract accurately the stress intensity factor and the T-Stress for fractured engineering materials is very significant in the decision-making process for in-service engineering components, mainly for their functionality and operating limit. The subject of computational fracture mechanics in engineering make this possible without resulting to expensive experimental processes. In this thesis, the Finite Block Method (FBM) has been developed for the meshless study of interface stationary crack under both static and dynamic loading in bi-materials. The finite block method based on the Lagrangian interpolation is introduced and the various mathematical constructs are examined. This includes the use of the mapping technique. In a one-dimensional and a two-dimensional case, numerical studies were performed in order to determine the interpolation error. The finite block method in both the Cartesian coordinate and the polar coordinate systems is developed to evaluate the stress intensity factors and the T-stress for interface cracks between bi-materials. Using the William’s series for bi-material, an expression for approximating the stress and displacement at the interface crack tip is established. In order to capture accurately the stress intensity factors and the T-stress at the crack tip, the asymptotic expansions of the stress and displacement around the crack tip are introduced with a singular core technique. The accuracy and capability of the finite block method in evaluating interface cracks is demonstrated by several numerical assessments. In all cases, comparisons have been made with numerical solutions by using the boundary collocation method, the finite element method and the boundary element method, etc

Software for evaluating probability-based integrity of reinforced concrete structures

In recent years, much research work has been carried out in order to obtain a more controlled durability and long-term performance of concrete structures in chloride containing environment. In particular, the development of new procedures for probability-based durability design has proved to give a more realistic basis for the analysis. Although there is still a lack of relevant data, this approach has been successfully applied to several new concrete structures, where requirements to a more controlled durability and service life have been specified. A probability-based durability analysis has also become an important and integral part of condition assessment of existing concrete structures in chloride containing environment. In order to facilitate the probability-based durability analysis, a software named DURACON has been developed, where the probabilistic approach is based on a Monte Carlo simulation. In the present paper, the software for the probability-based durability analysis is briefly described and used in order to demonstrate the importance of the various durability parameters affecting the durability of concrete structures in chloride containing environment

On tracking arbitrary crack path with complex variable meshless methods

This study presents a numerical modelling framework based on the complex variable meshless methods, which can accurately and efficiently track arbitrary crack paths in two-dimensional linear elastic solids. The key novelty of this work is that the proposed meshless modelling scheme enables a direct element-free approximation for the solutions of linear elastic fracture mechanics problems. The complex variable moving least-squares approximation with a group of simple complex polynomial basis is applied to implement this meshless model, with which the fracture problems with both stationary or progressive cracks are considered and studied. The effects of choosing different definitions of weighted complex variable error norm and different forms of complex polynomial basis on the computational accuracy of crack tip fields and crack paths prediction are analyzed and discussed. Five benchmark numerical examples were studied to demonstrate the superiority of the present complex variable meshless framework over a standard element-free Galerkin method in tracking arbitrary crack paths in two-dimensional elastic solids