Analytical Methods of Finding Stress Concentrations

[osnarf]

Hi everyone,

I'm an undergraduate student. A professor just signed me up to do a research project (my first) this semester, and I need to be able to apply elasticity to analytically find stress concentration factors in a specific geometry (I'll pm you if it matters which geometry) that the professor assigned as a project to me. I don't have any experience with the theory of elasticity, although I've taken an engineering undergraduate mechanics of materials course so I have some basic knowledge (but nothing on calculating stress concentration factors, just using them).

I have bought, borrowed from the professor, and checked out from the library a bunch of books on elasticity and advanced mechanics of materials that I'm going to start working through, but what concerns me is they don't really say explicitly what you'll be able to accomplish with them and the table of contents looks like gibberish to me since I'm not really familiar with the terminology. As far as I can tell, none of the tables of contents specifically mention finding stress concentration factors in arbitrary shapes; the chapters mostly seem to concentrate on a specific geometry.

I would like to know if I am looking in the right places and just don't know exactly what I'm looking for (hence, not seeing it) or should I find alternative sources? I just don't want to put a whole bunch of time into these books and realize I've been barking up the wrong tree. I'm not expecting there to be a cut and paste process for solving that kind of problem, I just want to make sure I'll be equipped with the right knowledge to figure it out. I've listed the books I have already at the bottom of the post.

Thanks a bunch

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The main book I am using is Green's.

-Partial Differential Equations for Engineers and Scientists (Farlow)
----^^Because I only have experience with Calculus of Variations solutions and was told I'd need PDE's

-Theoretical Elasticity (Green and Zerna)
-Elasticity - Tensor, Dyadic, and Engineering Approaches (Chou, Pagano)
-Advanced Mechanics of Materials and Applied Elasticity (Armenakas)
-Theory of Elasticity (Landau, Lifgarbages)
-Theory of Elasticity (Timoshenko)
-Intro to Continuum Mechanics and Elements of Elasticity/Structural Mechanics (Saouma)
-Introduction to Continuum Mechanics (Lai, Krempl, Rubin)
-Introduction to Tensor Calculus and Continuum Mechanics (Heinbockel)
-An introduction to Differential Geometry with Applications to Elasticity (Ciarlet)
-Elasticity - Theory, Applications, and Numerics (Sadd)

 

[TonyG]

Hi there,

It sounds like you have a great set of resources to start with for your research project. The books you have listed are all well-regarded and cover a wide range of topics related to elasticity and mechanics of materials. While they may not explicitly mention stress concentration factors in arbitrary shapes, they will provide you with the necessary theoretical background and tools to approach this problem.

In general, the theory of elasticity deals with the deformation and stress distribution in solid materials. This includes understanding how forces and loads are transmitted through a material, and how the material responds to these forces. Stress concentration factors are a key aspect of this, as they can help predict where and how a material may fail under certain loading conditions.

To specifically address your concern about finding stress concentration factors in arbitrary shapes, I would recommend focusing on the chapters and sections of these books that cover stress analysis and stress concentration. This may include topics such as Hooke's law, stress and strain tensors, and Mohr's circle. Additionally, you may want to look for chapters that discuss finite element analysis, as this method can be used to analyze complex geometries and calculate stress concentration factors.

It may also be helpful to reach out to your professor or a mentor in this field for guidance on specific chapters or sections of these books that would be most relevant to your project. They may also have additional resources or tips for approaching this problem.

Overall, it seems like you are on the right track with the resources you have chosen. Don't get discouraged if it takes some time to fully understand the material - elasticity and stress analysis can be complex topics, but with persistence and practice, you will be able to apply these concepts to your project successfully.

Best of luck with your research project!