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The discussion about deriving the sensitivity of compliance began from the previous article. This time, I would like to take a break from the derivation of sensitivity and explain the Lagrange multiplier method itself. Please feel free to download and take a look. [Contents] ■ Episode 24: Lagrange Multiplier Method *For more details, please refer to the PDF document or feel free to contact us.

• Structural Analysis

In the previous article, we introduced the Lagrange multiplier method as a condition that solutions must satisfy in optimization problems with equality constraints. This time, we will apply that concept to derive the sensitivity of compliance. Please feel free to download and take a look. [Contents] ■ Episode 25: Sensitivity of Compliance Part 3 "Lagrange Multiplier Method" *For more details, please refer to the PDF document or feel free to contact us.

• Structural Analysis

In the previous articles, we explained the compliance and its sensitivity when introducing two-dimensional design variables for a one-dimensional cantilever beam. This time, we will finally replace the design variables from a finite-dimensional vector to an infinite-dimensional function and construct the problem. Please feel free to download and take a look. [Contents] ■ Episode 26 Sensitivity of Compliance Part 4 "Problems with Design Variables Represented by Functions" *For more details, please refer to the PDF materials or feel free to contact us.

• Structural Analysis

Last time, we discussed how to define the Lagrange function to determine the sensitivity of compliance in a one-dimensional cantilever beam, using design variables represented as a function of cross-sectional area. This time, let's look at the approach based on the calculus of variations to derive the stationary conditions and the derivatives with respect to the cross-sectional area. Please feel free to download and take a look. [Contents] ■ Episode 27: Sensitivity of Compliance Part 5 "Derivation of Sensitivity with Respect to the Function Representing Cross-Sectional Area" *For more details, please refer to the PDF document or feel free to contact us.

• Structural Analysis

Previously, we introduced shape optimization for model correlation of vibration characteristics on our company website. In the article, we mentioned something called MAC (Modal Assurance Criterion), and in this article, we will explain it. Please feel free to download and take a look. [Contents] ■ Episode 28: About MAC *For more details, please refer to the PDF document or feel free to contact us.

• Structural Analysis

This time, I will discuss the idea related to the optimization problem of a function that takes values within a certain specified range, specifically focusing on the sigmoid function. When solving non-parametric optimization problems using the H1 gradient method, we consider that the initial value of the function, which serves as the design variable, is given, and we update the design variable by adding an incremental opening number to it. Therefore, this function must be an element of a linear space. I will carefully explain the concept of linear space as a review. Please feel free to download and take a look. [Contents] ■ Episode 29: Sigmoid Function *For more details, please refer to the PDF document or feel free to contact us.

• Structural Analysis

This time, I will explain the plugin feature of OPTISHAPE-TS. The plugin feature is designed for users to utilize their own evaluation functions in the shape optimization of OPTISHAPE-TS. I hope to convey that it can be quite challenging when you actually try to implement it. Please feel free to download and take a look. [Contents] ■ Episode 30: About the Plugin Feature *For more details, please refer to the PDF document or feel free to contact us.

• Structural Analysis

As mentioned in previous articles, non-parametric structural optimization reduces to the problem of finding the optimal function. In fact, when it comes to gradient methods, they are applied not only in design problems such as shape optimization and topology optimization but also in various fields of function optimization. This time, I will briefly introduce one example of identifying muscle activity during human swallowing movements. Please feel free to download and take a look. [Contents] ■ Episode 31: On Function Optimization and Its Applications *For more details, please refer to the PDF document or feel free to contact us.

• Structural Analysis