修正梯度弹性理论及其应用(英文版)

本书通过定义内部长度 尺度向量，并认为应变能密 度同时取决于应变张量和应 变梯度张量，提出了一种新 的理论——修正梯度弹性理 论 (Modified Gradient Elasticity，MGE)。该理论 能够有效描述微纳结构力学 行为中的尺寸效应及其耦合 效应，对研究微纳结构力学 响应及宏——细观关联提供 理论工具。该理论夯实了材 料(结构)在微观尺度的力学 理论基础，切实为高阶连续 介质理论在微纳米尺度力学 的发展做出了贡献。全书共 分四个部分，包括修正梯度 弹性理论(MGE)的提出、 MGE伯努利-欧拉梁模型、 MGE铁木辛柯梁模型和 MGE理论的拓展。本书充分 考虑了读者的需求，以独特 的视角对相关领域进行了深 度剖析。内容既有理论支撑 又有实际案例，使读者在阅 读过程中既能掌握专业知识 ，又能借鉴实际操作经验。 本书适用于力学专业的研究 生和博士生、从事高阶连续 介质理论研究和应用的学者 以及从事微纳米器件设计、 制造和防护方面的科研人员 和技术专家。

Contents Chapter 1 Introduction 1.1 An overview of higher-order continuum theory 1.2 Basic equations of the modified gradient elasticity (MGE) 1.2.1 Modified constitutive equations of gradient elasticity 1.2.2 Principle of virtual work: equilibrium equation and boundary conditions 1.3 Outline of this book Chapter 2 Micro-scale Bernoulli-Euler beam model based on MGE 2.1 Purpose of developing a micro-scale Bernoulli-Euler beam model 2.2 The governing equation and the boundary conditions for the bending problem 2.3 Numerical example of cantilever beams 2.3.1 Boundary conditions statement 2.3.2 Case 1: bending moment loading 2.3.3 Case 2: concentrated force loading 2.4 Comparison and discussion on the size effect 2.4.1 The comparison of micro-beam models 2.4.2 The influence of the internal length scales compared in different direction 2.4.3 Features Chapter 3 Thermal buckling of micro-scale Bernoulli-Euler beams based on MGE 3.1 Purpose of developing the thermal buckling model 3.2 The governing equation and boundary conditions 3.3 Numerical examples of different supported beams 3.3.1 Case 1: hinged-hinged micro-beams 3.3.2 Case 2: clamped-hinged micro-beams 3.3.3 Case 3: clamped-clamped micro-beams 3.4 A comparison of the thermal buckling model with other models 3.5 Chapter summary Chapter 4 Buckling of micro-scale thin-walled Bernoulli-Euler beams based on MGE 4.1 Purpose of developing the buckling model 4.2 Formulations and solution methodology 4.2.1 Governing equations and boundary conditions 4.2.2 Understanding of the governing equations 4.2.3 Solution methodology 4.3 Size effect of the critical buckling load and the buckling modes 4.4 A comparison of the buckling model with other models 4.5 Chapter summary Chapter 5 Thermal post-buckling of micro-scale Bernoulli-Euler beams based on MGE 5.1 Purpose of developing the thermal post-buckling model 5.2 The governing equations and boundary conditions 5.3 General solution of the thermal post-buckling 5.3.1 General solution for micro-beams with immovable axial boundary condition 5.3.2 Analytical solution for hinged-hinged micro-beams 5.3.3 Analytical solution for clamped-clamped micro-beams 5.4 Thermal post-buckling behavior of different supported micro-beams 5.5 Size effect and geometrically nonlinear effect on the thermal post-buckling 5.6 Chapter summary Chapter 6 Thermoelastic damping of micro-scale Bernoulli-Euler beams based on MGE 6.1 Purpose of developing the thermoelastic damping model 6.2 The governing equations and boundary conditions 6.3 Heat conduction equation considering strain gradients