Part10  Types of structural analysis and required material data

Contents

1. What is structural analysis?

2. Types of structural analysis (linear structural analysis, nonlinear structural analysis)

3. Applied structural analysis (dynamic analysis, thermal stress analysis)

4. Summary

What is structural analysis?

CAE structural analysis (stress analysis) is an analysis performed to confirm the effects of loads on structures and their components (deformation behavior, internal deformation state of parts, safety). It analyzes whether the design specifications for achieving the product's purpose and function are problem-free in terms of structural mechanics. Specifically, it verifies whether the structure is designed to maintain sufficient strength and durability by visualizing deformation behavior and stress distribution using structural analysis.
It is also used to investigate the cause of damage to a product when it is damaged during testing or an accident. It is an essential technology in manufacturing.

The most basic type of structural analysis is linear structural analysis. Linear structural analysis is an analysis that calculates static deformation behavior assuming elastic properties. In design, deformation and stresses for loads under design conditions must fall within elastic deformation, and structural shapes are designed and materials are selected to achieve this.

Other methods include nonlinear structural analysis that considers plastic deformation of materials due to large deformation, dynamic analysis that considers instantaneous loading (impact loading), and creep analysis that evaluates the creep effect caused by prolonged loading.
In real products, the loads acting on them change over time, creep phenomena occur with long-term use, and dynamic phenomena occur due to instantaneous loading. However, in the short-term range, when the response to loading is not significant or in steady state, it is treated as a static phenomenon. This allows for more efficient structural analysis since the boundary conditions are less complex and the computational load is lower than for dynamic phenomena.

The next section describes the types of structural analysis often used.

Types of structural analysis

One of the most important input items for structural analysis is the stress-strain curve (SS curve). A stress-strain curve is a graphical representation of the relationship between strain and stress when a material is deformed, and its shape differs depending on the material. For example, Figure 1 shows the stress-strain curve of stainless steel.
Material properties obtained from stress-strain curves as materials deform are essential information in structural analysis.

■ Linear structural analysis

1. Overview

Linear structural analysis is an analytical method that assumes that the deformation and stresses in a structure are sufficiently small that failure will not occur. As shown in Fig. 1, there is a proportional relationship between stress and strain within a range of small deformation (strain), and this region is called the elastic region. Linear structural analysis is an analysis method that assumes the properties of this elastic region. This analysis method is used in many situations because it requires fewer input conditions and less analysis time.

2. Required Data

CAD data, Young's modulus, Poisson's ratio, load boundary conditions

3. Results

Deformation behavior, displacement, stress distribution, strain, etc.

4. Points to note

This analysis is based on the assumption that loads, restraint conditions, etc. do not change over time.  Since the analysis is performed within a small range of deformation, it is not possible to analyze the state of fracture, etc.

 

■ Nonlinear structural analysis

1. Overview

Nonlinear structural analysis is an analysis method that considers large deformation and rotational behavior of structures (= geometric nonlinearity) and assumes that materials deform to within their plastic range (= material nonlinearity). In many cases, the analysis of actual phenomena will be nonlinear, so these nonlinearities must be taken into account in order to calculate more realistic phenomena in the analysis.

• Material Nonlinearity
  The region where the stress-strain relationship (SS curve) is no longer proportional after the yield point of a material is called the plastic region. Considering the SS curve, which includes this plastic region, as a physical property is called material nonlinearity. 
• Geometric Nonlinearity
  This method is used to account for cases where large deformations or rotational behavior cause the direction of loads to change from before to after deformation (see figure below). This method is used when large changes occur in members, such as large deformations that can be visually confirmed.

2. Required Data

Young's modulus, Poisson's ratio, SS curve (true stress-strain)

3. Results

Stress distribution, deformation amount, deformation mode

4. Points to note

When creating SS curves from tensile testing, the strain obtained by dividing the acquired displacement by the original length is called “nominal strain,” and the stress obtained by dividing the acquired load by the cross-sectional area before deformation is called “nominal stress. When performing a structural analysis that considers plastic deformation, which assumes large deformation, SS curves created with nominal stress and nominal strain cannot accurately represent the deformation behavior. Nominal strain must be converted to true strain and nominal stress to true stress, respectively for use in structural analysis.

Applied structural analysis

■ Dynamic analysis (impact analysis)

1. Overview

This analysis is used when loads are applied instantaneously and abruptly, such as in the case of a collision. It is used when such a situation is assumed in the product specifications, or to investigate the cause of failure.

2. Required Data

CAD data, Young's modulus, Poisson's ratio, density, load boundary conditions, (possibly also initial velocity and acceleration conditions)

3. Results

Deformation behavior, displacement distribution, velocity distribution, acceleration distribution, stress, strain

4. Points to note

Plastics has the property that material properties vary depending on the deformation rate (strain rate dependence). Therefore, if the deformation rate at the measurement point is high, SS curves obtained from tensile testing at low speeds may not be accurate for analysis. Analysis accuracy can be improved by using a high-speed tensile tester to obtain SS curves at high strain rates and incorporating them into the input information for structural analysis.

 

■ Thermal stress analysis

1. Overview

As shown in the figure below, materials expand as they warm up and contract as they cool down. This structural analysis takes into account expansion and contraction caused by temperature changes.

2. Required Data

CAD data, Young's modulus, Poisson's ratio, linear expansion coefficient, initial temperature, final temperature

3. Results

Deformation behavior, stress distribution, strain distribution, displacement distribution, temperature distribution

4. Points to note

If an object is in an unrestrained free state, it expands without resistance and thermal stress does not occur. However, thermal stress can occur if the object is constrained, if the temperature distribution within the object is uneven, or if the object is a structure composed of different materials. Therefore, if an object is expected to be used in a high-temperature environment, it is often necessary to perform a thermal stress analysis that takes into account the effects of thermal expansion.​

Summary

Various methods of structural analysis and the information required/obtained for each method were introduced.In any structural analysis, CAD data, physical properties (Young's modulus, Poisson's ratio), and loading boundary conditions are the minimum necessary information, so be sure to prepare them in advance. 
Applied structural analysis, such as nonlinear analysis and dynamic analysis, has the potential to provide behavior closer to actual phenomena, but the information that must be prepared in advance often presents a high hurdle to modeling. It is often possible to study smoothly by first conducting analysis using a simplified linear structural analysis and then gradually increasing the complexity of the model by following the steps.​

 

In the next part, we will discuss creep and fatigue analysis of plastics, which we could not fully introduce in this issue. Please look forward to it!