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**Structural Analysis and Optimization**

**COURSE TITLE****: **Structural Analysis and Optimization

**LECTURER:** Huang Hai, Chen Shen-yan

**HOURS:** 50

**CREDITS: **3

**COURSE DESCRIPTION**

The structural system is one of the most important sub-systems of a flight vehicle, which provides enough strength and stiffness for the vehicle to work properly, as well as space for other equipments or sub-systems attached together. However, the structural system usually takes a large part of weight, so the advanced structural analysis and design techniques that are crucial for reducing weight are constantly concerned to aerospace structural designers.

The purpose of this course is to provide some basic knowledge and methods of structural analysis and optimization. The structural analysis is focused on Finite Element Method (FEM) that nowadays is widely applied in aerospace and civil structural engineering. The course will introduce how the structural responses including deformation, stress distribution, etc. are calculated with on FEM. Based on FEM and combined with mathematical optimum theory, in the course, the structural optimization problems are established, which is to find a design that has the minimum structural weight and satisfied all requirements such as strength and stiffness. Some typical structural optimization methods are then discussed in the course, besides, the FEM analysis software Patran/Nastran is also introduced to the students，which contains some practice course hours to use the software in Lab.

**COURSE OBJECTIVE**

The purpose of this course is to provide some basic knowledge and methods of structural analysis and optimization. Though the course, a student is required to learn how to find the structural responses including deformation, stress distribution, etc. with FEM. Then he is further required to study reducing the structural weight with some typical structural optimization methods. Besides, the course will also train the student to use FEM analysis software Patran/Nastran with some practice course hours.

**CONTENTS AND ARRANGEMENTS**

1 Introduction and related mathematical basis (6hrs)

1.1 What is optimization?

1.2 Mathematical basis

1.3 Structural optimization model and its characteristics

2 Rudiment and structural analysis(8 hrs)

2.1 Truss structure

2.2 Plane problem

3 Sensitivity analysis(6 hrs)

3.1 The first order derivative of displacement

3.2 The first-order derivative of stress and frequency

3.3 The second order of displacement and stress

4 Criterion method and the approximation concept (6 hrs)

4.1 Full stress method

4.2 uniformed criterion method

4.3 The approximation concept

5 Algorithms to seek optimum(12 hrs)

5.1 Optimization for unconstrained problems

5.2 Optimization for constrained problems

6 Dual method (6 hrs)

6.1 Taylor expansion of different media variables

6.2 Dual theory and dual method

7 Two-level multipoint approximation method (4 hrs)

7.1 Multipoint approximation approach

7.2 Concept of two level multipoint approximation approach

8 Optimization example of satellite structure（2hrs）

9 Practice of Msc.Patran/Nastran (16hrs, As a coupling course, 1 credit)

9.1Softare introduction

9.2The process of structural modeling

9.3Explain with typical examples

9.4Practice

**TEACHING METHODS**

1. Lecture

2. Show and practice the FEA software Patran/Nastran

3. Home work and project

**COURSE ASSESSMENT**

1. Submitting a project of structural analysis with Patran/Nastran 20%

2. Writing test for basic concepts and knowledge (30%).

3. Providing a finely report to summarizing the course contents or discuss a special problem selected by students 50%

**PREQUISITE**

1. Theoretical Mechanics;

2. Material Mechanics;

3. Linear Algebra;

4. (Mathematical Programming in the best case).

**TEXTS**

[1] Huang Hai, Modern Structure Design Technology, Lecture material

[2]Chen Shenyan，Material for Msc.Patran/Nastran Practice

**REFERENCES**

Students need to read 2 or more reference papers in structural optimization, which can be searched by themselves or by teacher.