Mechanics of Deformable Structures: Part 2 from edX

In this course: (1) you will learn to model the multi-axial stress-strain response of isotropic linear elastic material due to combined loads (axial, torsional, bending); (2) you will learn to obtain objective measures of the severity of the loading conditions to prevent failure; (3) you will learn to use energy methods to efficiently predict the structural response of statically determinate and statically indeterminate structures.

This course will give you a foundation to predict and prevent structural failure and will introduce you to energy methods, which form one basis for numerical techniques (like the Finite Element Method) to solve complex mechanics problems

This is the third course in a 3-part series. In this series you will learn how mechanical engineers can use analytical methods and “back of the envelope” calculations to predict structural behavior. The three courses in the series are:

Part 1 – 2.01x: Elements of Structures. (Elastic response of Structural Elements: bars, shafts, beams).

Part 2 – 2.02.1x Mechanics of Deformable Structures: Part 1. (Assemblages of Elastic, Elastic-Plastic, and Viscoelastic Structural Elements).

Part 3 – 2.02.2x Mechanics of Deformable Structures: Part 2. (Multi-axial Loading and Deformation. Energy Methods).

These courses are based on the first subject in solid mechanics for MIT Mechanical Engineering students. Join them and learn to rely on the notions of equilibrium, geometric compatibility, and constitutive material response to ensure that your structures will perform their specified mechanical function without failing.

What's inside

Learning objectives

Hooke’s law for isotropic linear elastic materials and homogeneous problems in linear elasticity. pressure vessels. superposition of loading conditions.
Traction on a face. stress transformation. principal stress components. stress and strain invariants. tresca and mises yield criteria.

Elastic strain energy. castigliano methods. potential energy formulations. approximate solutions and the rayleigh ritz method

Hooke’s law for isotropic linear elastic materials and homogeneous problems in linear elasticity. pressure vessels. superposition of loading conditions.
Traction on a face. stress transformation. principal stress components. stress and strain invariants. tresca and mises yield criteria.
Elastic strain energy. castigliano methods. potential energy formulations. approximate solutions and the rayleigh ritz method

Syllabus

Unit 0: Review of Prerequisites. Integration of field variables. Introduction to MATLAB. Review of 2.01x: structural elements in axial loading, torsion, bending. Review of 2.02.1x: equilibrium and compatibility in 2D elastic assemblages.

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Builds upon knowledge from prerequisite courses, offering a deeper dive into multi-axial loading, deformation, and energy methods, which are essential for advanced structural analysis

Explores energy methods, providing a foundation for understanding numerical techniques like the Finite Element Method, which is widely used in engineering practice

Examines failure theories, including Tresca and Mises yield criteria, which are critical for designing structures that can withstand complex loading conditions and prevent failure

Requires prior knowledge from 'Elements of Structures' and 'Mechanics of Deformable Structures: Part 1', so learners should ensure they have a solid foundation in these topics first

Includes an introduction to MATLAB, so learners without prior experience may need to invest additional time in learning this software

Based on the first subject in solid mechanics for MIT Mechanical Engineering students, which may be too theoretical for some learners

Reviews summary

Rigorous advanced solid mechanics

According to learners, this course, Mechanics of Deformable Structures: Part 2, provides a rigorous and challenging deep dive into advanced solid mechanics concepts, particularly multi-axial loading, failure theories, and energy methods. Many students found the material, especially the homework problems and quizzes, to be quite difficult, often requiring significant time commitment. It is widely stated that strong prerequisites in mathematics (calculus, linear algebra) and the preceding courses in the series (Parts 1 & 2) are essential. Despite the difficulty, reviewers highlight the course's value in building a strong theoretical foundation, particularly for understanding numerical methods like Finite Element Analysis (FEA). Overall, it's seen as a demanding but highly rewarding course for those serious about the field.

Requires solid math and prior mechanics knowledge.

"Ensure you are very strong in calculus and linear algebra before taking this."

"You absolutely need to have completed Part 1 and Part 2, and understood them well."

"Lack of necessary prerequisites made the course much harder than it needed to be."

Valuable foundation for numerical methods like FEA.

"The energy methods units are particularly useful for anyone going into FEA."

"Gave me the necessary background to understand the basis of Finite Element Method."

"Understanding Castigliano's theorems and potential energy methods was key for my later FEA studies."

Excellent for understanding core mechanics principles.

"Provides a really solid theoretical background in multi-axial stress and strain."

"This course is great for building a strong understanding of the underlying principles."

"Helped solidify my grasp on energy methods and their applications."

Moves quickly through complex topics.

"The course moves very quickly, making it hard to keep up sometimes."

"Lectures pack a lot of information into each segment."

"Felt rushed through some of the more complex derivations."

The course content and problems are demanding.

"The material covered is very challenging, especially the problem sets."

"I found the quizzes and homework quite difficult and time-consuming."

"Definitely not a course for the faint of heart, requires significant effort."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Mechanics of Deformable Structures: Part 2 with these activities:

Review Statics and Mechanics of Materials

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Reinforce your understanding of fundamental concepts like stress, strain, and equilibrium, which are essential for grasping the multi-axial loading and energy methods covered in this course.

Browse courses on Mechanics of Materials

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Review key concepts from your statics and mechanics of materials textbook.
Work through example problems related to stress, strain, and free body diagrams.
Focus on topics like axial loading, torsion, and bending.

Read 'Mechanics of Materials' by James M. Gere and Barry J. Goodno

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Use this book to reinforce your understanding of stress-strain relationships and failure criteria.

View Mechanics of Materials on Amazon

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Read the chapters related to stress transformation and failure theories.
Work through the example problems in the book.
Compare the book's approach to the course material.

Solve multi-axial stress problems

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Practice applying stress transformation equations and failure criteria to various multi-axial loading scenarios to improve your problem-solving skills.

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Find practice problems online or in textbooks.
Solve the problems, paying attention to units and sign conventions.
Check your answers against the solutions.

Four other activities

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Read 'Advanced Mechanics of Materials' by Arthur P. Boresi and Richard J. Schmidt

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Use this book to deepen your understanding of advanced topics.

View Advanced Mechanics of Materials on Amazon

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Read the chapters related to energy methods and failure theories.
Compare the book's approach to the course material.
Work through the example problems in the book.

Create a presentation on energy methods

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Develop a presentation explaining Castigliano's theorem and the Rayleigh-Ritz method to solidify your understanding and improve your communication skills.

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Research Castigliano's theorem and the Rayleigh-Ritz method.
Create slides explaining the concepts and providing examples.
Practice presenting the material to a friend or colleague.

Design a pressure vessel

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Apply your knowledge of multi-axial stress and failure theories to design a pressure vessel that meets specific performance requirements.

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Define the design requirements for the pressure vessel.
Calculate the stresses and strains in the vessel under pressure.
Select a material and wall thickness to ensure the vessel does not fail.
Document your design calculations and material selection process.

Create a Finite Element Analysis (FEA) Model

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Develop an FEA model of a structure subjected to multi-axial loading to validate analytical solutions and explore complex geometries.

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Choose an appropriate FEA software package (e.g., ANSYS, Abaqus).
Create a geometric model of the structure.
Apply appropriate boundary conditions and loads.
Run the analysis and interpret the results.
Compare the FEA results to analytical solutions.

Career center

Learners who complete Mechanics of Deformable Structures: Part 2 will develop knowledge and skills that may be useful to these careers:

Stress Analyst

A stress analyst evaluates the integrity of mechanical components and structures under various loading conditions. This often involves predicting stress and strain distributions within a structure to ensure it can withstand applied forces without failure. This course is especially relevant, as it helps build a foundation in understanding multi-axial stress-strain responses, using failure theories, and applying energy methods to predict structural behavior. The course's coverage of stress transformation, principal stress components, and design limits on multi-axial stress, including Tresca and Mises yield criteria, provides indispensable knowledge for a stress analyst.

See salaries and explore the career path for Stress Analyst

Structural Engineer

Structural engineers design and assess the safety and stability of structures such as buildings, bridges, and frameworks. A key aspect of their work is understanding how structures respond to various loads and preventing failure. This course helps structural engineers to predict and prevent structural failure using analytical methods. The study of energy methods, which form the basis for numerical techniques, will prove valuable. The course's focus on multi-axial loading and deformation, coupled with energy methods, directly supports the core responsibilities of a structural engineer.

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Finite Element Analyst

Finite element analysts use computer simulations to predict how a product reacts to real-world forces, vibration, heat, fluid flow, and other physical effects. The work involves creating a computer model of the part or design you want to test, and then dividing it into small elements. The course is particularly relevant as it introduces energy methods. Energy methods form one basis for numerical techniques like the finite element method to solve complex mechanics problems. In addition, the course covers the analysis of structures under multi-axial loading conditions, which is often encountered by finite element analysts.

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Mechanical Engineer

Mechanical engineers research, design, develop, manufacture, and test mechanical devices and systems. A core skill for mechanical engineers is the ability to predict how structures behave under different loading conditions. This course helps mechanical engineers use analytical methods to predict structural behavior. The course's content, including its focus on multi-axial stress-strain responses and energy methods, provides the foundation required to ensure that mechanical designs perform their specified functions without failing. Mechanical engineers will find the course's treatment of failure theories to be very important.

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Aerospace Engineer

Aerospace engineers design, develop, and test aircraft, spacecraft, satellites, and missiles. The design of lightweight yet strong structures is critical in aerospace engineering. This course helps aerospace engineers predict and prevent structural failure. The knowledge of multi-axial loading, stress transformation, and failure theories is important when designing aerospace components that must withstand extreme conditions. Aerospace engineers may find the discussion of energy methods to be helpful when thinking about reducing structural weight.

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Civil Engineer

Civil engineers plan, design, and oversee the construction and maintenance of infrastructure projects such as roads, bridges, dams, and buildings. Understanding structural behavior under various loads is fundamental to civil engineering. This course may be useful for civil engineers, as it introduces analytical methods to predict structural behavior. The course's content, specifically its focus on multi-axial stress-strain responses, failure theories, and energy methods, helps to ensure the safety and longevity of civil infrastructure.

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Product Design Engineer

Product design engineers are involved in the process of conceptualizing, designing, and developing new products. They need a strong understanding of material properties and structural behavior to ensure products are durable and reliable. This course helps design engineers predict the behavior of structural components, and prevent structural failure. The course's focus on multi-axial loading and energy methods is relevant to product design, helping engineers to create innovative and structurally sound products.

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Automotive Engineer

Automotive engineers design and develop vehicles and their components. They focus on performance, safety, and efficiency. Understanding how vehicle components respond to stress and strain is important for ensuring vehicle safety and durability. This course may be useful to automotive engineers because of its coverage of multi-axial stress-strain responses and failure theories. The course's content provides foundational knowledge for designing robust and reliable automotive structures.

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Reliability Engineer

Reliability engineers assess and improve the reliability of systems, products, and processes. They analyze potential failure modes and develop strategies to prevent failures and improve overall performance. This course may be relevant because it helps build a foundation in understanding structural behavior and predicting potential failure. The course's treatment of failure theories provides valuable tools for reliability engineers, enabling them to better assess and mitigate risks to system and product reliability.

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Materials Scientist

Materials scientists research and develop new materials and processes. This often involves understanding the mechanical properties of materials under different conditions. This course may be useful for materials scientists, as it introduces the study of multi-axial stress and strain. The course's treatment of Hooke’s law for isotropic linear elastic materials, stress transformation, and failure theories helps gain insights into material behavior under complex loading scenarios. Further study and an advanced degree is typically required.

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Engineering Consultant

Engineering consultants provide expert advice and guidance to clients on a variety of engineering projects. They use their knowledge to solve complex problems, and may work across many industries. This course may be useful for engineering consultants, as it introduces analytical methods to predict structural behavior. The course's content on multi-axial stress-strain responses, failure theories, and energy methods provides valuable tools for addressing structural challenges in consulting projects.

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Design Engineer

Design engineers create technical drawings and specifications for new products. They use computer-aided design (CAD) software and other tools to develop detailed designs that meet specified requirements. This course may be useful for design engineers, as it helps build a foundation in understanding structural behavior. The course's discussion of multi-axial loading and energy methods is relevant to design, helping engineers to create functional and structurally sound designs.

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Test Engineer

Test engineers develop and implement testing procedures to evaluate the performance and reliability of products. They analyze test data and identify areas for improvement. This course may be helpful for test engineers because of its introduction of analytical methods to predict structural behavior. The course's focus on multi-axial stress-strain responses and failure theories provides relevant knowledge to test structural integrity effectively.

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Research and Development Engineer

Research and development engineers conduct research and develop new technologies and products. They design and conduct experiments, analyze data, and create prototypes. This course may be useful for research and development engineers because of its coverage of energy methods. The course's content provides valuable insights into structural behavior, and may help in the development of new, high-performance systems.

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Engineering Technician

Engineering technicians assist engineers in the design, development, testing, and manufacturing of products and systems. They typically work under the supervision of engineers. This course may be useful for engineering technicians, as it covers the elastic response of structural elements. The course's content on multi-axial stress-strain responses will prove helpful for technicians supporting engineers in structural analysis and design.

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Mechanics of Deformable Structures

Part 2

What's inside

Learning objectives

Syllabus

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Reviews summary

Rigorous advanced solid mechanics

Activities

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