Tiantang Yu

Geometrically nonlinear analysis of functionally graded plates using isogeometric analysis

Purpose – The purpose of this paper is to propose an efficient and accurate numerical model that employs isogeometric analysis (IGA) for the geometrically nonlinear analysis of functionally graded plates (FGPs). This model is utilized to investigate the effects of boundary conditions, gradient index, and geometric shape on the nonlinear responses of FGPs. Design/methodology/approach – A geometrically nonlinear analysis of thin and moderately thick functionally graded ceramic-metal plates based on IGA in conjunction with first-order shear deformation theory and von Karman strains is presented. The displacement fields and geometric description are approximated with nonuniform rational B-splines (NURBS) basis functions. The Newton-Raphson iterative scheme is employed to solve the nonlinear equation system. Material properties are assumed to vary along the thickness direction with a power law distribution of the volume fraction of the constituents. Findings – The present model for analysis of the geometricall...

Free Vibration Analyses of FGM Thin Plates by Isogeometric Analysis Based on Classical Plate Theory and Physical Neutral Surface

The isogeometric analysis with nonuniform rational B-spline (NURBS) based on the classical plate theory (CPT) is developed for free vibration analyses of functionally graded material (FGM) thin plates. The objective of this work is to provide an efficient and accurate numerical simulation approach for the nonhomogeneous thin plates and shells. Higher order basis functions can be easily obtained in IGA, thus the formulation of CPT based on the IGA can be simplified. For the FGM thin plates, material property gradient in the thickness direction is unsymmetrical about the midplane, so effects of midplane displacements cannot be ignored, whereas the CPT neglects midplane displacements. To eliminate the effects of midplane displacements without introducing new unknown variables, the physical neutral surface is introduced into the CPT. The approximation of the deflection field and the geometric description are performed by using the NURBS basis functions. Compared with the first-order shear deformation theory, the present method has lower memory consumption and higher efficiency. Several numerical results show that the present method yields highly accurate solutions.

Numerical modeling of 3-D inclusions and voids by a novel adaptive XFEM

A novel adaptive XFEM using hexahedron elements for inclusions and voids of composite materials is presented.A posteriori error estimation based on recovery strain allows ones to obtain a desired accuracy with one or two trials.Variable-node hexahedron transition elements are used to treat the mismatching problems of different meshes.Single and multiple inclusions and voids in composites are modeled accurately and efficiently. This paper describes an adaptive numerical framework for modeling arbitrary inclusions and holes in three-dimensional (3-D) solids based on a rigorous combination of local enriched partition-of-unity method, a posterior error estimation scheme, and the variable-node hexahedron elements. In this new setting, a posteriori error estimation scheme driven by a recovery strain procedure in terms of extended finite element method (XFEM) is taken for adaptive purpose (local mesh refinement). Refinement is only performed where it is needed, e.g., the vicinity of the internal boundaries, through an error indicator. To treat the mismatch of different meshes-scale in 3-D, the variable-node hexahedron elements based on the generic point interpolation are thus integrated into the present formulation. The merits of the proposed approach such as its accuracy, effectiveness and performance are demonstrated through a series of representative numerical examples involving single and multiple inclusions/holes in 3-D with different configurations. The obtained numerical results are compared with reference solutions based on analytical and standard non-adaptive XFEM methods.

3-D elasto-plastic large deformations

Numerical analysis of 3-D elasto-plastic large deformations is presented.Isogeometric analysis based on Bzier extraction of NURBS is extended to 3-D elasto-plastic large deformation.The Bzier extraction operator can integrate isogeometric analysis into the existing finite element codes.Higher accuracy is obtained as compared with that of finite element method. This paper is devoted to the numerical simulation of elasto-plastic large deformation in three-dimensional (3-D) solids using isogeometric analysis (IGA) based on Bzier extraction of NURBS (non-uniform rational B-splines), due to some inherently desirable features. The Bzier extraction operation decomposes the NURBS basis functions into a set of linear combination of Bernstein polynomials and a set of C0-continuity Bzier elements. Consequently, the IGA based on Bzier extraction of NURBS can be embedded in existing FEM codes, and more importantly, as have been shown in literature that higher accuracy over traditional FEM can be gained. The main features distinguishing between the IGA and FEM are the exact geometry description with fewer control points, high-order continuity, high accuracy. Unlike the standard FEM, the NURBS basis functions are capable of precisely describing both geometry and solution fields. The present kinematic is based on the Total Lagrange description due to the elasto-plastic large deformation with deformation history. The results for the distributions of displacements, von Mises stress, yielded zones, and force-displacement curves are computed and analyzed. For the sake of comparison of the numerical results, the same numerical examples have additionally been computed with the FEM using ABAQUS. IGA numerical results show the robustness and accuracy of the technique.

Role of material combination and new results of mechanical behavior for FG sandwich plates in thermal environment

Abstract Functionally graded materials often operate in high temperature environment, and have been extensively used in a variety of engineering applications including nuclear power plant and spacecraft. In this paper, we present new numerical results of mechanical behavior for functionally graded sandwich plates in high temperature. We investigate material combinations and stress distribution of sandwich plates with FGM faces. One interesting physical point is captured. It shows that not all sandwich FGM plates possess similar mechanical behavior and performance in high temperature. We address the importance of material combinations, which significantly affect the mechanical behavior of resulting sandwich plates. The transition point in the mechanical response is found, which only occurs to some particular material combinations. All numerical results are calculated by a finite element model with selective reduced numerical integration based on the first-order shear deformation theory. A parametric study is also carried out to demonstrate the impact of severe high temperature on the mechanical behavior of sandwich plates.

The extended finite element method (XFEM) for discontinuous rock masses

Purpose – The purpose of this paper is to achieve numerical simulation of discontinuous rock masses.Design/methodology/approach – The extended finite element method (XFEM) was used. Discontinuities (such as joints, faults, and material interfaces) are contained in the elements, thus the mesh can be generated without taking into account the existence of discontinuities. When one element contains no discontinuity, the displacement function is degenerated into that of the conventional finite element. For the element containing discontinuities, the standard displacement‐based approximation is enriched by incorporating level‐set‐based enrichment functions that model the discontinuities, and an element subdivision procedure is used to integrate the domain of the element.Findings – Mesh generation can be simplified considerably and high‐quality meshes can be obtained. A solution with good precision can also be achieved. It is concluded that the XFEM technique is especially suitable in simulating discontinuous ro...

Implementation of isogeometric boundary element method for 2-D steady heat transfer analysis

Formulation of isogeometric boundary element method for steady heat transfer is derived.Geometry data can be taken directly from CAD.High accuracy of heat transfer problems can be obtained with less degree of freedom.Advantages of the common boundary representation of the IGA and BEM are possessed. In this paper, the recently developed hybrid numerical method based on isogeometric analysis (IGA) and boundary element method (BEM), named as IGABEM, is further extended to study steady heat transfer problems in two dimensions (2D). The IGA employs spline basis functions (e.g., NURBS) as shape functions for geometric description and field approximation. The NURBS only describe the boundary of objects, and the BEM also directly deals with the boundaries. Therefore, the combined IGABEM is highly attractive as it takes advantages of the common boundary representation of both the IGA and the BEM. The formulation of IGABEM for steady heat transfer is derived, and its performance and accuracy are verified through numerical test cases by comparing the obtained results with analytical and finite element method solutions. The convergence of the developed approach for steady heat transfer problems is also analyzed. The computer codes of the IGABEM developed for steady heat transfer analysis can be accessed at: http://www.idmes.cn/codes.html.

Mesoscopic Numerical Simulation of Stratified Rock Failure Using Digital Image Processing

This paper presents a digital image processing (DIP) based finite difference method (FDM) and makes the first attempt to apply the new method to the failure process of stratified rocks from Chinese Jinping underground carves. In the method, the two-dimensional (2D) inhomogeneity and mesostructures of rock materials are first identified with the DIP technique. And then the binarization image information is used to generate the finite difference grids. Finally, the failure process of stratified rock samples under uniaxial compression condition is simulated by using the FDM. In the DIP, an image segmentation algorithm based on seeded region growing (SRG) is proposed, instead of the traditional threshold value method. And with the new method, we can fully acquire the inhomogeneous distributions and mesostructures of stratified rocks. The simulated macroscopic mechanical behaviors are in good agreement with the laboratory experimental observation. Numerical results show that the proposed DIP based FDM is suitable for the failure analysis of stratified rocks because it can fully take into account the material heterogeneity, and the anisotropy of stratified rocks is also disposed to some extent.

Influence of heterogeneity on mechanical and acoustic emission behaviours of stratified rock specimens

Abstract This paper investigates the influence of heterogeneity on mechanical and acoustic emission (AE) behaviours of stratified rock specimens under uniaxial compression using a digital image processing (DIP)-based finite difference method (FDM). In the DIP, a developed image segmentation algorithm based on seeded region growing (SRG) is proposed to fully acquire the mesostructure of stratified rock specimens, instead of the traditional threshold value method. To sufficiently capture the heterogeneity of stratified rock, Weibull statistical manner is adopted to describe mechanical properties of each material component. Three schemes are adopted to study the effect of heterogeneity with different homogeneity index and different mesostructure under two compression loading conditions. The results show that heterogeneity has a great influence on the mechanical and AE behaviours of stratified rock. As the homogeneity of material components increases, the peak strength and brittleness of rocks increase, and the macro elastic modulus improves as well. Simultaneously, the AE modes change from swarm shock to main shock. Under the same component content, the macro-property is better while the component distribution is concentrative relatively, especially to the property of strength. For the coupling effect of mesostructure and heterogeneity arising from material components, mesostructure is considered to cause the visible increase of AE counts. And the numerical results agree well with the previously numerical results and experimental data.