For me, it took four years to earn an engineering degree. But that is just step one on a long journey. Most professionals like me spend a lifetime learning engineering concepts and applying them throughout their careers; especially as you start to go beyond the basic and general concepts to the more specialized areas like Structural Simulation and Finite Element Analysis (FEA).
对我来说，获得工程学位花了四年时间。但这只是漫长旅程的第一步。大多数像我这样的专业人士都花了一生的时间学习工程概念，并在他们的整个职业生涯中应用它们;尤其是当您开始超越基本和一般概念，进入结构仿真和有限元分析 （FEA） 等更专业的领域时。

Personally, I dedicated a large part of my engineering career exclusively to thoroughly understanding FEA technology as best I could. I can say from that experience it’s easy to believe that as an engineer we’ve forgotten more than we could ever remember.
就我个人而言，我在工程职业生涯的很大一部分时间里都致力于尽可能彻底地了解 FEA 技术。我可以说，从那次经历中，我很容易相信，作为一名工程师，我们忘记的东西比我们记得的要多。

In this article, I want to continue to discuss engineering concepts as I reintroduce you to some of the biggest forgotten secrets of simulation. By the end, you will be able to go from theoretical to practical and effectively set up FEA studies using SOLIDWORKS Simulation.
在本文中，我想继续讨论工程概念，同时再次向您介绍仿真中一些被遗忘的最大秘密。最后，您将能够从 THEORETICAL 过渡到实践，并使用 SOLIDWORKS Simulation 有效地设置 FEA 算例。

1.     Stress  1. 压力

Stress quantifies how a material responds to forces. It measures the intensity of a force on an object. It’s not unlike how we humans experience and respond to stress. External forces or pressures can cause changes to us just like to materials. It’s best to think about this on the microscopic level as the actual atoms move around (react) when acted on by an external force. The simplest definition of stress is shown in the equation below which describes how stress is related to a force acting on it.
应力量化了材料对力的响应方式。它测量物体上力的强度。这与我们人类体验和应对压力的方式没有什么不同。外力或压力会像材料一样导致我们发生变化。最好在微观层面上考虑这一点，因为实际原子在受到外力作用时会四处移动（反应）。应力的最简单定义显示在下面的方程中，它描述了应力与作用在其上的力的关系。

Stress is often measured in PSI or Pascals. From an engineering perspective, stress could be used to determine if something will hold up or break. Consider a bar made of steel and chocolate – it’s easy to break the chocolate bar with your hands but nearly impossible (unless you’re Superman) to break a steel bar the same way. This is an example of how different levels of stress cause different things to break — low stress breaks chocolate while steel can hold up to higher stresses.
压力通常以 PSI 或帕斯卡为单位。从工程角度来看，应力可用于确定某物是否会支撑或断裂。考虑一下由钢和巧克力制成的巧克力棒——用手打破巧克力棒很容易，但几乎不可能（除非你是超人）以同样的方式打破钢棒。这是一个例子，说明不同程度的压力如何导致不同的东西破裂——低应力会破坏巧克力，而钢可以承受更高的压力。

Components of Stress in 3D Space. (Image: Wikimedia Commons, Sanpaz.)
3D 空间中的应力分量。（图片：Wikimedia Commons， Sanpaz。

2.     Strain  2. 应变

Strain quantifies how a material’s shape changes when it’s stressed. This is basically doing a comparison of the initial shape (unstressed) to the change in shape when loaded (stressed). It’s a unitless value that can be thought of as a percentage of change in shape. The simple equation for this is shown below.
应变量化了材料在受力时形状的变化。这基本上是将初始形状 （无应力） 与加载 （有应力） 时的形状变化进行比较。它是一个无单位的值，可以看作是形状变化的百分比。此的简单方程如下所示。

3.     Hooke’s law (Robert Hooke)
3. 胡克定律 （Robert Hooke）

Hooke’s law is a core concept for simulation because it introduces us to the concept of “elasticity” which states that the deformation of an elastic material is proportional to the applied force — within the elastic limit for the material (more on this later).
胡克定律是仿真的核心概念，因为它向我们介绍了“弹性”的概念，该概念指出弹性材料的变形与施加的力成正比 - 在材料的弹性极限内（稍后会详细介绍）。

The simple equation for Hooke’s law is shown above, which relates force to material stiffness (k) and its displacement (x). It essentially shows the proportionality of a force to displacement – the greater the force the more the shape will change or deform. In engineering context, Hooke’s law is written as shown below where most importantly the stiffness value (k) is written as E which is the Young’s modulus.
胡克定律的简单方程如上所示，它将力与材料刚度 （k） 及其位移 （x） 联系起来。它基本上显示了力与位移的比例——力越大，形状的变化或变形就越多。在工程环境中，胡克定律的写法如下所示，其中最重要的是刚度值 （k） 写成 E，即杨氏模量。

4.     Young’s modulus (Thomas Young)
4. 杨氏模量 （Thomas Young）

Young’s modulus is another core concept for simulation. It is a material property which describes how stress and strain are related for a particular material. Young’s modulus (E), sometimes known as the modulus of elasticity, is shown below in its simplest form:
杨氏模量是仿真的另一个核心概念。它是一种材料属性，用于描述特定材料的应力和应变之间的关系。杨氏模量 （E），有时也称为弹性模量，以最简单的形式显示如下：

This characterizes the “stiffness” of a material where a higher value means a stiffer/stronger material and a lower value means a more flexible material. A few sample values are shown below notice how much stronger steel and aluminum are than something like wood.
这描述了材质的“刚度”，其中较高的值表示材质越硬/越强，而较低的值意味着材质越柔韧。下面显示了一些示例值，请注意钢和铝比木头等东西的强度要高得多。

5.     The stress – strain curve
5. 应力 - 应变曲线

The stress-strain curve is a plot that defines a material’s journey through loading. Think of it like a road map which defines how a material will perform. It’s built upon the above concepts. This graph is an essential piece to understanding how a material will behave and ultimately how much force (stress) it can withstand before it breaks. As an engineer or designer, you’ll want to stay well below the Yield Strength (except for some exceptions).
应力-应变曲线是定义材料加载过程的绘图。可以将其视为定义材质性能的路线图。它建立在上述概念之上。该图是了解材料的行为方式以及最终在断裂之前可以承受多少力（应力）的重要部分。作为工程师或设计师，您需要保持远低于屈服强度（除了一些例外）。

An example stress-strain curve. (Image: Stephen Petrock.)
应力-应变曲线示例。（图片：Stephen Petrock。

As shown above, there are distinct regions of the curve which are important to understand. Most important for SOLIDWORKS Simulation is the understanding of the linear and nonlinear (plastic) regions of the stress strain curve.  
如上所示，曲线的不同区域需要了解。对于 SOLIDWORKS Simulation 来说，最重要的是了解应力应变曲线的线性和非线性（塑性）区域。

6.     Linear versus nonlinear and elastic versus inelastic
6. 线性与非线性，弹性与非弹性

This is a good point in the article to begin discussing the capabilities of SOLIDWORKS Simulation and how they relate to the physics within a model. The linear region of the stress strain curve can be thought of as the zone of simple analysis with “small displacements.” It represents stresses below the yield point of a material. This is where any changes in shape are not permanent. The material will change shape (strain), but it will return to its original shape when it’s unloaded. The term for this is elastic deformation. For these models you can use SOLIDWORKS Simulation Standard.
这是本文开始讨论 SOLIDWORKS Simulation 的功能以及它们与模型中的物理特性之间的关系的一个很好的要点。应力应变曲线的线性区域可以被认为是具有“小位移”的简单分析区域。它表示低于材料屈服点的应力。这是形状的任何变化都不是永久性的。材料会改变形状 （应变），但在卸载时会恢复到原来的形状。术语是弹性变形。对于这些模型，您可以使用 SOLIDWORKS Simulation Standard。

However, anything beyond the yield point can be thought of as nonlinear. This is where the more advanced SOLIDWORKS Simulation Premium must be used. If a material is stressed to this region, it will not return to its original shape when its unloaded. This is known as permanent deformation. Think of when you significantly bend a paper clip it doesn’t return to its original shape. Another term for this is inelastic deformation.
但是，超出屈服点的任何内容都可以被视为非线性。这是必须使用更高级的 SOLIDWORKS Simulation Premium 的地方。如果材料受到该区域的应力，则它在卸载时不会恢复到其原始形状。这称为永久变形。想想看，当你大幅弯曲回形针时，它不会恢复到原来的形状。另一个术语是非弹性变形。

7.     Linear v nonlinear in SOLIDWORKS Simulation
7. SOLIDWORKS Simulation 中的线性与非线性

Here is a pro tip when using SOLIDWORKS Simulation Standard for linear static analysis. The “large displacement” option can be used to get a pseudo nonlinear answer without the nonlinear price. If you’ve used SOLIDWORKS Simulation, you’ve probably seen this message.
以下是使用 SOLIDWORKS Simulation Standard 进行线性静态分析时的专业提示。“large displacement” 选项可用于获得没有非线性价格的伪非线性答案。如果您已使用 SOLIDWORKS Simulation，则可能已看到此消息。

This option uses an iterative solver to gradually apply the load and recalculate the geometric stiffness of the model. This accounts for geometric nonlinearities but not the material nonlinearities if the material goes beyond the Yield Point.
此选项使用迭代求解器逐渐施加载荷并重新计算模型的几何刚度。如果材料超出屈服点，则这考虑了几何非线性，但不包括材料非线性。

8.     Hand calculation examples
8. 手牌计算示例

So how does this all come together to solve an engineering problem? Let’s answer that with an example that looks at the question: can our part withstand a given loading? Note that for the purposes of this article, we are going to solve this in the same order as SOLIDWORKS Simulation using the four equations shown above which are stiffness, change in shape and then stress. The simplified version of this FEA problem is illustrated below.
那么，这一切是如何结合在一起解决工程问题的呢？让我们用一个例子来回答这个问题：我们的零件能承受给定的载荷吗？请注意，在本文中，我们将使用上面显示的四个方程式（刚度、形状变化和应力），按照与 SOLIDWORKS Simulation 相同的顺序来求解此问题。此 FEA 问题的简化版本如下所示。

Problem Statement: Consider a steel rod 1 foot in length with a diameter of ¼”. Can it hold a load of 2,250 pounds?
问题陈述： 考虑一根 1 英尺长、直径为 1/4 英寸的钢棒。它能承受 2,250 磅的负载吗？

Step 0: Convert units & look up material properties.
步骤0：转换单位并查找材料属性。

The very first thing we do is convert to metric because it’s easier in the engineering world. So here are our converted inputs.
我们做的第一件事是转换为公制，因为它在工程领域更容易。所以这是我们转换后的输入。

• Length L = 1 foot = 0.3048 m
  长度 L = 1 英尺 = 0.3048 米
• Diameter D = ¼” = 0.00635 m
  直径 D = 1/4“ = 0.00635 米
• Force = F = 2,250 lb = 10,000 N
  力 = F = 2,250 磅 = 10,000 N
• Material Properties of Steel
  钢材的材料特性
  • Young’s Modulus (E) of 200 GPa (from SOLIDWORKS Material Library)
    杨氏模量 （E） 为 200 GPa（来自 SOLIDWORKS 材料库）
  • Yield Strength of 350 MPa (from SOLIDWORKS Material Library)
    屈服强度为 350 MPa（来自 SOLIDWORKS 材料库）

Step 1: Determine the stiffness of this scenario.
第 1 步：确定这种情况的刚度。

Starting with Hooke’s Law, we can rearrange to calculate the stiffness (K):
从胡克定律开始，我们可以重新排列以计算刚度 （K）：

Leverage the equations for stress and strain.
利用应力和应变方程。

Substitute into Hooke’s Law and leverage the stress strain relationship.
代入 Hooke 定律并利用应力应变关系。

Rearrange the equation to match Hooke’s Law.
重新排列方程以匹配胡克定律。

Thus,  因此

Step 2: Calculate the change in shape (solve for ∆L).
第 2 步：计算形状的变化（求解 ∆L）。

Step 3: Calculate the stress from the change of shape (strain).
第 3 步：根据形状变化（应变）计算应力。

Final step: Ensure the safety factor is greater than 1.
最后一步：确保安全系数大于 1。

Conclusion: The design will “hold up” (more on this below).
结论：设计将“站得住脚”（更多内容见下文）。

9.     Factor of safety  9. 安全系数

The final step in the above calculation introduced the concept of a factor of safety. With the factor of safety we can determine if the design will “hold up” by comparing the stress to the material limits. This is usually defined as:
上述计算的最后一步引入了安全系数的概念。利用安全系数，我们可以通过比较应力与材料极限来确定设计是否“站得住脚”。这通常被定义为：

By applying this safety factor equation, you’ll ensure that your design stays in the elastic region and therefore no permanent deformations occur.
通过应用这个安全系数方程，您将确保您的设计保持在弹性区域，因此不会发生永久变形。

10.                        Finite Element Analysis (FEA)
10. 有限元分析 （FEA）

SOLIDWORKS Simulation is a finite element analysis (FEA) tool. FEA is the technique to solve these engineering problems by breaking it down into small pieces, solving each piece, and then putting it all together to give you a complete result. The engineering problem is your model with the loadings. The small pieces are known as elements. A typical problem will have thousands of elements and there could be 30 equations per element. In other words, SOLIDWORKS Simulation does what we just did for the example problem but nearly a million times in a matter of seconds! That’s the power of a tool like SOLIDWORKS Simulation.  
SOLIDWORKS Simulation 是一种有限元分析 （FEA） 工具。FEA 是一种解决这些工程问题的技术，方法是将其分解成小块，解决每个部分，然后将它们放在一起，得到一个完整的结果。工程问题是您的模型和载荷。小块称为元素。一个典型的问题将有数千个单元，每个单元可能有 30 个方程。换句话说，SOLIDWORKS Simulation 可以完成我们刚刚对示例问题所做的操作，但在几秒钟内执行了近 100 万次！这就是 SOLIDWORKS Simulation 等工具的强大之处。