也就是说，如果您有一定的 ODE 求解器经验，那么 FEM 的基本思想相当简单。您能否告诉我们更多有关您的背景以及您真正想学什么的信息，以便我们推荐一些合适的资源？您想学习基础数学，还是只想学习一些将 FEM 应用于某一类问题的食谱？
Really understanding Finite Element Methods requires quite a bit of fairly advanced mathematics; unless you have a few years to devote to the cause, let's leave that aside for now.
That said, the basic ideas underlying FEM are fairly simple if you have some experience with ODE solvers. Can you tell us some more about your background and what you really want to learn so that we can suggest some appropriate resources? Do you want to learn the underlying mathematics, or do you just want to learn some cookbook recipes for applying FEM to a certain class of problem?
Your question is unclear. I don't know what you want to know, because it's impossible to tell what you're ignorant of here.
You don't deal with advanced math every day. What do you know about the finite element method? Here are topics you'll need to know:
Statics and dynamics; how to draw free body diagrams
Solid mechanics - strength of materials, elasticity,
Continuum mechanics for large strain models: Lagrangian and Eulerian formulations
Material models - elasticity and plasticity
Partial differential equations
Method of weighted residuals and integral equations
Linear algebra
Numerical methods
Geometric modeling - CAD for geometry and meshing for FEA models
Commercial or open source packages
You don't say whether you want to use a commercial package (ANSYS, NASTRAN, ABAQUS) or something that you'll write.
As far as references go, there are lots of books available now, but they aren't easy to read or absorb. I'd recommend T.J.R. Hughes' Dover book on the subject. It's cheap and good.
But it's not easy.
I just skimmed through the paper. It looks like a survey article, with nothing new to contribute to the state of the art. It covers a lot more than just small strain plasticity of metals. I see fabric models, large strain problems, etc.
It also mentions boundary element methods and finite difference methods. Do you want to know about those, too? Boundary element methods are completely different from finite elements. The former are based on Green's function formulations; the latter use method of weighted residuals.
The paper doesn't have a great deal of depth to it, but it's very broad. What do you want to know?
I don't think it's possible for someone with so little background to write their own. A better place to start would be FENICS.
A really good introduction to FEA for beginners is "Practical Stress Analysis with Finite Elements" by Bryan J Mac Donald. This concentrates on stress analysis but shows you how the method works from both a practical and a theoretical point of view. Unlike a lot of other books it is not specific to any particular software and it is written in plain, easy-to-understand language.
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真正理解有限元方法需要大量相当高级的数学知识；除非你有几年的时间来致力于这项事业，否则我们暂时把它放在一边。
也就是说，如果您有一定的 ODE 求解器经验，那么 FEM 的基本思想相当简单。您能否告诉我们更多有关您的背景以及您真正想学什么的信息，以便我们推荐一些合适的资源？您想学习基础数学，还是只想学习一些将 FEM 应用于某一类问题的食谱？
Really understanding Finite Element Methods requires quite a bit of fairly advanced mathematics; unless you have a few years to devote to the cause, let's leave that aside for now.
That said, the basic ideas underlying FEM are fairly simple if you have some experience with ODE solvers. Can you tell us some more about your background and what you really want to learn so that we can suggest some appropriate resources? Do you want to learn the underlying mathematics, or do you just want to learn some cookbook recipes for applying FEM to a certain class of problem?
你的问题不清楚。我不知道你想知道什么，因为你不可能知道你不知道什么。
你并不是每天都在处理高等数学。关于有限元法你了解多少？以下是您需要了解的主题：
您没有说明是否要使用商业软件包（ANSYS、NASTRAN、ABAQUS）或其他软件包你会写的。
就参考资料而言，现在有很多书籍可供参考，但它们并不容易阅读或吸收。我推荐 TJR Hughes 关于该主题的 多佛书籍。它又便宜又好。
但这并不容易。
我只是浏览了一下报纸。它看起来像是一篇调查文章，没有任何新内容可以对最新技术做出贡献。它涵盖的不仅仅是金属的小应变塑性。我看到了织物模型、大应变问题等。
还提到了边界元法和有限差分法。你也想了解这些吗？边界元方法与有限元完全不同。前者基于格林函数公式；后者使用加权残差的方法。
这篇论文没有太多深度，但它非常广泛。你想知道什么？
我认为背景如此之少的人不可能自己写。更好的起点是 FENICS。
Your question is unclear. I don't know what you want to know, because it's impossible to tell what you're ignorant of here.
You don't deal with advanced math every day. What do you know about the finite element method? Here are topics you'll need to know:
You don't say whether you want to use a commercial package (ANSYS, NASTRAN, ABAQUS) or something that you'll write.
As far as references go, there are lots of books available now, but they aren't easy to read or absorb. I'd recommend T.J.R. Hughes' Dover book on the subject. It's cheap and good.
But it's not easy.
I just skimmed through the paper. It looks like a survey article, with nothing new to contribute to the state of the art. It covers a lot more than just small strain plasticity of metals. I see fabric models, large strain problems, etc.
It also mentions boundary element methods and finite difference methods. Do you want to know about those, too? Boundary element methods are completely different from finite elements. The former are based on Green's function formulations; the latter use method of weighted residuals.
The paper doesn't have a great deal of depth to it, but it's very broad. What do you want to know?
I don't think it's possible for someone with so little background to write their own. A better place to start would be FENICS.
我可以推荐 Carlos A. Felippa 的有限元方法导论。它相对容易阅读。
您可以在此处找到它，各章链接在主页。
仅涵盖直接刚度法，考虑桁架变形而不考虑时间。
它遵循非常好的“实践”方法，并在 Mathematica 中提供示例，非常适合开发人员。
I can recommend Introduction to Finite Element Methods by Carlos A. Felippa. It is relativly easy to read.
You can find it here, the Chapters are linked on the main page.
Only the direct stiffness method is covered, think of deformations of trusses without time considerations.
It follows a very nice 'hands-on' approach with examples in Mathematica which are well suited for developer folks.
对于初学者来说，FEA 的一个非常好的介绍是“有限元实用应力分析 ”布莱恩·J·麦克唐纳德着。这集中于应力分析，但从实践和理论的角度向您展示了该方法是如何工作的。与许多其他书籍不同，它不特定于任何特定软件，并且以简单易懂的语言编写。
A really good introduction to FEA for beginners is "Practical Stress Analysis with Finite Elements" by Bryan J Mac Donald. This concentrates on stress analysis but shows you how the method works from both a practical and a theoretical point of view. Unlike a lot of other books it is not specific to any particular software and it is written in plain, easy-to-understand language.