# Stress Analysis in Mechanical Design

In the modern mechanical design environment, products must be brought to market with minimal testing and at the lowest possible development cost. As a result of this lean organization focus, the risk mitigation efforts of mechanical engineers who can competently analyze complex structures or mechanical devices continue to be recognized as an essential component of most mechanical design organizations.

##### Complete Details

This course is designed for the practicing engineer with an interest in the various aspects of stress analysis in mechanical engineering design, but who has had no solid experience or training in this important field. Topics include deterministic stress analysis, prevention of failure for ductile and brittle materials, material fatigue and fracture mechanics, numerical optimization, and analysis of bolted joints. Numerical optimization presents a fresh and interesting dimension to this course, in which state-of-the-art methodologies and software applications for performing analysis for design synthesis* *are presented. Optimization is becoming more and more essential in the modern product development environment as it frees engineers to do creative work by automating tedious operations.

Course topics are presented in such a manner as to have applicability across a broad spectrum of industries, based on the philosophy that a competent stress analyst should be able to analyze almost any mechanical system. Typical applications include the aerospace and automotive industries, most manufacturing industries where product certification through testing and analysis is required, and any industry involving mechanical components where public safety and/or product reliability are crucial.

The course is intended for design engineers who would like to become more familiar with the techniques and modern practices of stress analysis to help them be more efficient and productive in their work; mechanical engineers who have been out of college for a while and need to become more competent in the area of stress analysis due to a particular job assignment or new career opportunity that requires expertise in analyzing structures; and department managers whose staff is involved in mechanical design or stress analysis work.

##### Course Materials

Lecture notes are distributed on the first day of the course. These notes are for participants only and are not for sale.

##### Coordinator and Lecturer

**Dennis C. Philpot, MS, PE**, Senior Staff Engineer, Structural and Thermal Analysis, Alliant Techsystems, Woodland Hills, California. Mr. Philpot began his career in the aerospace industry at the Rocketdyne Division of Rockwell International in 1983, where he was involved in several diverse programs, including the Space Shuttle Main Engines, the National Aerospace Plane, and the International Space Station. In support of these programs, Mr. Philpot served as both a stress analyst and as a dynamics engineer. During the preliminary design phase of the Space Station program, he was the primary structural analyst to present briefings to the customer (NASA) for the Rockwell team. Utilizing both classical (hand) analyses and computer models, he was instrumental in solving a number of structural issues that surfaced in the program.

During the late 1990s, Mr. Philpot became involved with performing fighter aircraft structural analysis on two different prime contracts. These included the F/A 18 E/F program for Northrop-Grumman and the Joint Strike Fighter for Lockheed-Martin Skunk Works. He also served as a principal structural analyst on two launch systems—the Kistler reusable launch system and the Delta IV EELV developed by the Boeing Company. On each of these programs, he consistently demonstrated leadership and innovation in the analysis of primary and secondary structural components and set new standards in analysis report documentation.

In his current position, Mr. Philpot is responsible for the structural integrity of Alliant Techsystems (ATK) products and oversees the structural analyses performed by subcontractors that support ATK programs. He also serves as the test director for environmental testing (thermal and mechanical) that are conducted for the purpose of hardware development, acceptance, and qualification. Having performed structural analysis for over two decades and studied many volumes of analysis literature, Mr. Philpot has written internal procedures and created software tools for the analysis of various types of structural components. He has taught courses in mathematics, stress analysis, and dynamics in various venues over the past two decades; is a Registered Professional Engineer in the state of California; and has earned several NASA Technology Awards for demonstrating innovative ways of applying space technology to serve mankind. Mr. Philpot is a member of both the ASME and the AIAA.

##### Daily Schedule

*Day 1*

**Introduction **

- What Structures Do
- Why Structures Fail
- Analysis in the Mechanical Design Environment
- Vectorial and Analytical Mechanics
- Product Specification and Design Criteria
- Key Engineering Processes in Mechanical Design
- Modern Approaches to Structural Analysis
- Definitions and Terminology

**Engineering Mechanics Review**

- Units and Conversion Factors
- Introduction to Solid Mechanics
- The Importance and Usefulness of Free Body Diagrams
- Equations of Equilibrium
- Two-Dimensional Theory of Elasticity
- Constitutive Relations
- Equations of Compatibility
- The Airy Stress Functions
- Derivation of Sectional Properties
- Analysis of Trusses

—Method of Joints

—Method of Sections - Analysis of Beams

—Moment and Shear Diagrams

—Calculation of Stresses in Beams

—Analysis of Asymmetric Beams - Stability Analysis of Columns

—Euler Buckling Equation

—J.B. Johnson Formula - Analysis of Plates
- Analysis of Torsion Rods
- In-Class Examples

**Energy Methods in Mechanical Analysis**

- The Usefulness of Energy Methods
- Work Done by a Single Load
- Work Done by a System of Loads
- Energy Theorems
- The Principle of Stationary Potential Energy
- Strain Energy in a Variety of Structural Elements
- The Rayleigh-Ritz Method
- Lagrange’s Equations of Motion
- Finite Element Method Discussion
- Summary

*Day 1*

**Failure Prevention of Engineering Materials**

- The Stress Analyst’s Primary Task
- Deterministic vs. Probabilistic Stress Analysis
- Feasibility and the Technical Meaning of “Failure”
- Design Criteria and Product Specifications
- The Proper Use of Factors of Safety
- Computation of Margins of Safety
- Failure by Material Distortion
- Ductile Rupture after Extensive Deformation
- Sudden Fracture of Brittle Materials

—Assumption of Preexisting Flaws

—Without Preexisting Flaws - Progressive Fracture through Material Fatigue
- In-Class Examples

**Fundamentals of Deterministic Stress Analysis**

- Definition of Stress
- Hook’s Law
- Equilibrium of a 2-D Stress Element
- Derivation of the Principal Stresses and Principal Axes of a 2-D Stress Element
- Mohr’s Circle of Stress
- Static Failure Theories for Ductile Failure

—Maximum Shear Stress Theory

—Von Mises-Hencky Theory - Static Failure Theories for Brittle Failure

—Maximum Principal Stress Theory

—Mohr’s Failure Theory - Stress Concentration Factors in Mechanical Design
- Linear Elastic Fracture Mechanics (LEFM) Approach

—Historical Background of Fracture Mechanics

—The Column Analogy to Brittle Fracture

—Fracture Toughness as a Material Property

—Environmental Conditions that Affect Crack Propagation

—The Stress-Field Approach to Fracture Mechanics

—Computation of Stress Intensity Factors - In-Class Examples

**Analysis of Bolted Joints**

- Anatomy of a Bolted Joint (Free Body Diagram)
- Computation of Material Stiffness
- Estimating Joint Constants
- Determination of Preload
- The Bolted Joint Diagram
- Calculation of Critical External Load
- Failure Modes of Bolted Joints

—Failure of Bolt in Tension

—Failure of Bolt in Shear

—Failure of Bolt in Bending

—Failure of Net Section in Tension

—Failure of Net Section in Shear Tear-Out

—Failure of Material in Bearing

—Failure of Threads in Shear

—Failure Due to Combined Loading - Analysis of Bolts Loaded in Tension
- Analysis of Bolts Loaded in Shear
- Interaction Equation for Combined Loading
- Computation of Internal Thread Shear Strength
- In-Class Examples

*Day 3*

**Numerical Optimization**

- Introduction and Motivation
- The Optimization Problem

— Objective Functions, Design Variables and Constraints

— Design Variable Linking

— Implicit and Explicit Constraints - Unconstrained Design Problems
- Constrained Design Problems
- Optimization Software

— MathCad^{©}

— MatLab^{©}

—DOC^{©}and DOT^{©}

—NASTRAN Solution 200

—GENESIS^{©}

—Others - Structural Optimization
- The Finite Element Method
- Multidiscipline Design Optimization
- Examples Using DOT
^{©} - Examples Using FEA
- Summary

**Fatigue and Life Prediction Analysis **

- A Brief History of Fatigue Failure
- Definitions and Terminology
- Mechanism of Fatigue Failure
- Fatigue Stress Concentration Factor and Notch Sensitivity
- Fatigue Data from MIL-HDBK-5H
- Master Fatigue Diagrams
- Endurance Limit Modifying Factors
- Modified Goodman Approach
- Gerber Relation
- Fatigue Crack Propagation and Paris’s Law
- Damage Tolerance and Fracture Control
- In-Class Examples

**Documentation of Stress Analyses **

- Third Person, Past-Tense Writing Style
- Clarity
- Conciseness
- Continuity
- Objectivity
- Anatomy of a Typical Stress Analysis Report

**Closing Remarks **

**For more information contact the Short Course Program Office: **

shortcourses@uclaextension.edu | (310) 825-3344 | fax (310) 206-2815