《有限元法：理论、格式与求解方法（第2版）》- 巴特（Bathe）

需积分: 50 35 浏览量更新于2024-07-15 收藏 36.89MB PDF 举报

"Finite Element Procedures Second Edition.pdf" 是一本由Klaus-Jürgen Bathe教授编写的关于有限元方法的专业书籍。 Bathe教授是机械工程领域的权威，同时也是ADINA公司的创始人，该公司开发的ADINA软件是一款功能强大的多物理场分析工具，涵盖了结构、流体、热、电磁以及各种耦合场的分析。该书的中文版名为《有限元法：理论、格式与求解方法（第2版-上下册）》，由轩建平翻译。在ADINA公司的官方网站上，可以找到许多免费资源，包括本书的英文版、中文版、答案、程序以及麻省理工学院的相关课程视频。有限元方法(Finite Element Method, FEM)是一种数值计算方法，常用于解决复杂的工程和物理问题。它将连续区域划分为许多互不重叠的子区域（有限元），然后对每个元素内部的偏微分方程进行近似求解，最后通过接口条件将所有元素的解组合成整个区域的解。这种方法能够有效地处理复杂几何形状和非线性问题，广泛应用于结构力学、流体力学、热传导、电磁学等领域。本书第二版于2014年出版，截至2016年进行了第四次印刷。书中详细介绍了有限元方法的基本理论、离散过程、公式构建以及求解策略。读者可以通过学习本书掌握如何应用有限元方法来解决实际工程中的问题，涉及的内容可能包括： 1. 有限元方法的基本概念：介绍有限元的起源、基本原理及其在工程中的应用背景。 2. 离散化技术：讲解如何将连续区域划分为有限个简单的几何元素，并构建有限元网格。 3. 弱形式与变分原理：阐述如何从连续问题的强形式转化为便于数值求解的弱形式。 4. 节点插值函数与基函数：介绍不同类型的有限元基函数，如拉格朗日基函数、 Hermite基函数等，以及它们如何用于近似解决方案。 5. 公式构建：讨论如何构造线性或非线性系统方程，包括刚度矩阵、质量矩阵和荷载向量的形成。 6. 求解算法：涵盖直接法、迭代法等求解线性系统的策略，以及如何处理非线性问题。 7. 各类物理场的有限元分析：详细介绍结构力学、流体力学、热传导和电磁学等领域的有限元应用。 8. 结果后处理：讲述如何评估和可视化有限元求解的结果，包括误差分析和收敛性检查。此外，书中可能还包含了许多实用的编程示例和练习题，帮助读者深入理解并掌握有限元方法的实践应用。通过 Bathe教授的这本著作，无论是初学者还是经验丰富的专业人士，都能获得宝贵的有限元分析知识。

Sec.

1.2

Physical Problems, Mathematical Models, the Finite Element Solution

Physical problem

Mathematical model

Governed

differential equations

Assumptions

• Geometry

• Kinematics

• Material law

• Loading

• Boundary conditions

•

Etc.

Change

physical

problem

Improve

mathematical

model

r------------------- -----------------------------------

I I

: Finite element solution I

l Choice

l • Finite elements I

: • Mesh density :

Finite

I • Solution parameters l

element I Representation

solution l • Loading l

of l • Boundary conditions Refine mesh, :

mathematical : •

Etc.

solution parameters, :

model

l etc. l

I I

I i Assessment of accuracy offlnke l

---1_____

[

:~:~:-·:_~~~~~~-::~~~h:-~~~~~~~:~

_________________

Interpretation of results

---

Refine

analysis

Design

improvements

Structural optimization

Figure

1.1

The process of

finite

element analysis

Let us emphasize that, by our analysis,

can of course only obtain insight into the

physical problem considered:

cannot predict the response

the physical problem

exactly because it is impossible to reproduce even

the most refined mathematical model

all the information that is present in nature and therefore contained in the physical problem.

Once a mathematical model has been solved accurately and the results have been

interpreted,

may well decide to consider next a refined mathematical model in order

increase our insight into the response of the physical problem. Furthermore, a change

the

physical problem may

be necessary, and this in turn will also lead

additional mathemat-

ical models and finite element solutions (see Fig.

1.1

The key step in engineering analysis

therefore choosing appropriate mathematical

models. These models will clearly be selected depending on what phenomena are to be

An Introduction to the

Use

Finite Element Procedures

Chap.

predicted, and

is most important to select mathematical models that are reliable and

effective in predicting the quantities sought.

To define the reliability and effectiveness

a chosen model we think

a very-

comprehensive

mathematical model

the physical problem

and

measure the response

our chosen model against the response

the comprehensive model. In general, the very-

comprehensive mathematical model is a fully three-dimensional description that also in-

cludes nonlinear effects.

Effectiveness

a mathematical model

The

most effective mathematical model for the analysis is surely that one which yields

the required response to a sufficient accuracy and at least cost.

Reliability

a mathematical model

The chosen mathematical model

reliable

the required response is known

predicted within a selected level

accuracy measured

the response

the very-

comprehensive mathematical model.

Hence to assess the results obtained by the solution

a chosen mathematical model,

it may

necessary to also solve higher-order mathematical models, and we may well think

(but

course not necessarily solve) a sequence

mathematical models that include

increasingly more complex effects. For example, a

beam

structure (using engineering termi-

nology) may first be analyzed using Bernoulli beam theory, then Timoshenko beam theory,

then two-dimensional plane stress theory, and finally using a fully three-dimensional

continuum model, and in each case nonlinear effects may be included. Such a sequence

models is referred to as a hierarchy

models (see K. I. Bathe, N. S. Lee, and

L. Bucalem

[A]). Clearly, with these hierarchical models the analysis will include ever more complex

response effects but will also lead to increasingly more costly solutions. As is well known,

a fully three-dimensional analysis is about an order

magnitude more expensive (in

computer resources and engineering time used) than a two-dimensional solution.

Let

us consider a simple example to illustrate these ideas.

Figure l .2(a) shows a bracket used

support a vertical load. For the analysis, we need

choose a mathematical model. This choice must clearly depend on what phenomena are

be predicted and

the geometry, material properties, loading, and support conditions

the bracket.

have indicated in Fig. l.2(a) that the bracket is fastened

a very thick steel

column. The description "very thick"

course relative to the thickness t and the height

the bracket.

translate this statement into the assumption that the bracket

fastened

to a (practically) rigid column. Hence we can focus

our

attention on the bracket by applying

Hrigid

column boundary condition"

it.

(Of

course, at a later time, an analysis

the

column may

required, and then the loads carried by the two bolts, as a consequence

the load

will need

be applied

the column.)

also assume that the load W

applied very slowly. The condition

time "very

slowly" is relative

the largest natural period

the bracket;

that

is, the time span over

which the load Wis increased from zero

its full value

much longer than the fundamen-

tal period

the bracket.

translate this statement into requiring a static analysis (and not

a dynamic analysis).

Sec.

1.2

Physical Problems, Mathematical Models, the Finite Element Solution

full bracket. This model should include the two bolts fastening the bracket to the (assumed

rigid) column as well as the pin through which the load Wis applied. The three-dimensional

solution of this model using the appropriate geometry and material data would give the

numbers against which we would compare the answers given in ( 1.1) and ( 1.2

Note that

this three-dimensional mathematical model contains contact conditions (the contact is

between the bolts, the bracket, and the column, and between the pin carrying the load and

the bracket) and stress concentrations in the fillets and at the holes. Also,

the stresses

are high, nonlinear material conditions should be included in the model.

course, an

analytical solution

this mathematical model is not available, and all we can obtain is a

numerical solution.

describe in this book how such solutions can

calculated using

finite element procedures, but we may note here already that the solution would be rela-

tively expensive in terms

computer resources and engineering time used.

Since the three-dimensional comprehensive mathematical model is very likely too

comprehensive a model (for the analysis questions we have posed), we instead may consider

a linear elastic two-dimensional plane stress model as shown in Fig. 1.2(c). This mathemat-

ical model represents the geometry

the bracket more accurately than the beam model and

assumes a two-dimensional stress situation in the bracket (see Section 4.2). The bending

moment at section

and deflection under the load calculated with this model can be

expected to be quite close

those calculated with the very-comprehensive three-

dimensional model, and certainly this two-dimensional model represents a higher-order

model against which we can measure the adequacy

the results given in ( 1.1) and ( 1.2).

course, an analytical solution

the model

not available, and a numerical solution must

be sought.

Figures 1.3(a) to

(e)

show the geometry and the finite element discretization used in

the solution

the plane stress mathematical model and some stress and displacement

results obtained with this discretization. Let

note the various assumptions

this math-

ematical model when compared

the more comprehensive three-dimensional model dis-

cussed earlier. Since a plane stress condition is assumed, the only nonzero stresses are

Txx,

Tyy, and

Txy,

Hence we assume that the stresses

Tyz, and

Tz.x

are zero. Also, the actual bolt

fastening and contact conditions between the steel column and the bracket are not included

(a)

Geometry

bracket

obtained from a

CAD

program

Figure

1.3

Plane

stress

analysis

bracket

Fig.

1.2.

AutoCAD

was

used

create the

geometry,

and

ADINA

was

used

for

the

finite

element

analysis.

剩余1055页未读，继续阅读

万志康

粉丝: 0
资源: 1

《有限元法：理论、格式与求解方法（第2版）》- 巴特（Bathe）

FLUENT流体模拟软件教程：用户指南与应用案例

DS2.5 Windows安装教程：避开360，成功设置许可证

小木虫论坛中文期刊点评爬虫工具开发

[muchong.com]有限单元法程序计.zip_fem fortran_finite element_有限元单元法_有限元法

[muchong.com]化学反应.pdf

[muchong.com]腐蚀模块.pdf

[muchong.com]计算流体力学.pdf

anacus的英文操作指导[muchong.com]GUI.pdf

[muchong.com]AUTOLISP语言参考.pdf

[muchong.com]hypermesh经典基础教程.pdf

最新资源