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### 1. Mechanics and Simulation

The basis of mechanical engineering is mechanics. Mechanics includes statics, dynamics, solid mechanics (material mechanics and structural mechanics), fluid mechanics, and thermodynamics. In the curriculum, you learn statics and dynamics first. Statics deals with the case where nothing happens because all forces are balanced. On the other hand, dynamics deals with the case where forces are not balanced, and the unbalanced force causes something to happen. Most people say that dynamics is more complicated and difficult than statics when they study theories.

What is Dynamics Analysis? Just as there are statics and dynamics in mechanics, there are static analysis and dynamic analysis in simulations. The static analysis analyzes the steady state in which forces are balanced in an object or system. This is a state where there is no change no matter how much time passes. Therefore, changes in time are not considered. On the contrary, dynamic analysis analyzes the moving state of an object or system. At this point, time or frequency is considered to express motion. The dynamic analysis is generally more complicated because it has more variables to consider than does the static analysis. This is why the dynamic analysis requires more analysis time and know-how than the static analysis. <static analysis vs dynamic analysis>

Those who use simulation think that static analysis is relatively easy, and they use it more often. There are two reasons why they use static analysis more.

(1) People are more familiar to the static analysis than they are to the dynamic analysis because statics is often learned before dynamics in the curriculum. Also, because the dynamic analysis becomes complicated when it goes deeper, they often learn only the basics and move on.

(2) They think that the static analysis costs (in terms of time, effort, and money) less than the dynamic analysis. This is because they learned from books and papers that the dynamic analysis requires more analyzing time and know-how than the static analysis.

In many cases, people learn the static analysis in college first. In “Thinking in Bets: Making Smarter Decisions When You Don't Have All the Facts” , Annie Duke said, “People often have a bias that considers the information they encounter first is to be more correct than that what they encounter later.” Such a bias seems to be applied in the selection of either the static or dynamic analysis. In other words, a person who learned the static analysis first can argue that, even if he or she encounters a situation in which the dynamic analysis is needed, it is sufficient with the static analysis. Of course, the reverse is possible as well. Anyone who has come to know the dynamic analysis first can argue that, even if in the situation for which the static analysis is enough, the dynamic analysis should be applied. It is necessary to pay attention to the information bias in order to correctly determine which is more beneficial in a given situation.

Considering the amount of information, the difference between the static analysis and the dynamic analysis becomes more apparent. Even if they search the Internet or related literature, there is much more information they can get about the static analysis.This also leads to a bias towards choosing static analysis over dynamic analysis.

### 2. Difference Between Static Analysis vs Dynamic Analysis

Since the conceptual difference between the static analysis and the dynamic analysis has been described above, I will explain the difference using a formula below. Let us look at the force formula and the spring formula below.

Force formula: F= ma (m, mass; a, acceleration)

Spring formula: F= kδ (K, spring constant; δ, spring deformation) The original form of the spring formula is the force equation, F= kδ+ma+cv. In this formula, velocity (v) and acceleration (a) are related to time (t). If not in motion, ma and cv can be regarded as 0 and omitted. Then, the equation becomes F= kδ. Solving this equation is the static analysis. On the other hand, the dynamic analysis solves the entire equation F= kδ+ma+cv without omitting any terms.

Among several types of simulation methods, in the structural analysis, the static analysis solves F= kδ, and the dynamic analysis solves F= kδ+ma+cv. Out of these, as methods of the dynamic analysis, there are modal analysis, harmonic response analysis, forced vibration analysis, spectrum analysis, and transient analysis.

As shown in the equation, the static analysis is a part of the dynamic analysis. Since it is assumed that there is no change over time, the formula is simplified and can speed up computer calculations. However, the information that can be obtained from the result is limited.

Written by Taero Cha (Director of China Business Division)