Composite structure analysis by hand 1

[WK95]

There are lots of resources for structural analysis using FEA but I don't want to even dabble with FEA until I can confidently get ballpark answers the old fashioned ways (Microsoft excel, pen and paper, calculator, etc).

Any resources for that?

Here's what I'm looking for
1) Resources for learning structural analysis of composite material structures the old fashioned way (pen and paper and some spreadsheets)
2) Mechanics of materials textbooks that use the generalized hooke's law
3) Structural analysis of fuselages that don't have a simple circular cross section

I've got a couple of great books that provide an introduction to composite materials for micromechanics, macromechanics, ply mechanics, and such. but they lack information on the methods for structural analysis of composite structures.

 

[RPstress]

Bruhn—Analysis of Flight Vehicle Structures. NB: you will have to adapt the methods from isotropic metal to orthotropic laminates but this is usually doable with common sense and knowledge of structures. Gere and Timoshenko (Mechanics of Materials) is often also useful for structural elements. Kaw and Barbero are two composites references which also have some simple structural analysis. And never forget Professor Gordon's three books (particularly "The New Science of Strong Materials or Why You Don't Fall Through the Floor" and "Structures or Why Things Don't Fall Down"—I can't recommend these two strongly enough although they're light on how to do analysis, though very relevant to composites). Also handy is the FPL Wood Handbook (for a copy Google forest products laboratory wood handbook wood as an engineering material).

 

[adfergusson]

I commend your intention to gain a solid grasp of the fundamentals of the mechanics of composite materials. If you are looking to, for example, be able to predict the response of a composite plate to a pressure load then there is a book by Reddy that is useful Link

We've used the solutions in the book to, for example, work out how different elements are handling through thickness shear and what proportion of discrepancies between models we get are down to element formulation, mesh size, etc... However, composites are complicated so analytical solutions often involve some variation the theme of multiplying laminated plate equations by some function, integrating by parts to get the equation in its weak integral form and implementing the boundary conditions... If you're doing this then you're not far off using the FE method anyway.

If you intend to develop yourself towards being able to do useful analysis on composite structures then you will have to get comfortable with numerical methods.If your concerned that FE is a bit of a black box then why not start with using finite differences to solve some simple problems? Once you're happy with FD then you could look at getting your head around finite volume and then/ or finite element methods? The Reddy book will be useful again here to as it goes through various means of handling through thickness deformation that you can then relate to how shell and continuum finite elements might behave when through thickness stresses are meaningful.

PS If you really want to get into composites then I'd suggest that learning about both experimental testing and manufacturing methods for composites (the performance of composite materials is inextricably intertwined with how they are made) are worth setting time aside for too.

 

[WK95]

I've picked up a copy of Reddy and boy, is it heavy on theory and serious math. Definitely grad school stuff (I'm only in undergrad). Other than that, the CLPT section isn't too hard to wrap my head around.

For now, my plan is to start out by developing a small (4" diameter at most), simple cylindrical fuselage structure using quasi-isotropic laminates. From there, I then optimize the laminate. Won't get me the lightest structure but it'll have to do until I figure out the more complex techniques.

Can you recommend any resources about finite differences as applied to mechanics of materials?

 

[ESPcomposites]

If you are looking for practical stuff, then look into books that are written by engineers. If you are more interested in theory, then look into books written by professors. While the difference between the two for metals is not vast, there is a major difference for composites. In general, academic books pay little attention to notches, impact damage, joints, etc., which are some of the major sizing drivers for composites. Engineers don't usually care about the unnotched (pristine) capability of structures. Unfortunately, the classical approaches for metals do not carry over well to composites. Composites must consider: notch sensitivity, bearing-bypass, BVID strength, large notch strength, interlaminar stresses, variety of failure modes/mechanisms, etc.).

Brian

http://www.espcomposites.com

 

[adfergusson]

I'd recommend YouTube as a starting point for getting into numerical methods! I'd start simple with solving simple beam theory problems using Euler's method. There's a Khan Academy video on Euler's method that gives a simple and clear example of it; watch it and see if you can work out how to use the same approach to solve some beam theory ODEs (e.g Euler-Bernouli vs Timoshenko beam theory). THis will give you some practice and help you understand the implications of the underlying assumptions of mechanics theories. Move onto this playlist to get some further understanding of other means of solving ODEs; Link

Once you're happy with solving ODEs you can then move onto solving PDEs; a set of videos to get your feet wet on this, and from the same guy; is here: Link

If you're already comfortable with CLPT then you could try and apply some of the techniques in this video series to some simple problems. I'd choose to use worked examples from Reddy so that you can compare you're numerical results with analytical solutions

I, personally, think the treatment of FD, FV and FE methods is a bit lightweight but the videos are a good starting point. There are loads of other vides series out there; have a look for stuff that suits you. I've put a number of my students, new hires and interns onto Prof Gilbert's MITx/EdX 18.085 in the past (Link)to learn more about numerical methods but am now evaluating this course as training material: Link It's quite fluids focused but the bonus is that it's got some interesting practical examples and you get useful Python practice thrown in with it (Disclosure; I'm a big fan of Python/SciPy/MatPlotLib/etc stacks and find it very annoying that most engineering grads come out of College with a need for thousands of dollars worth of MatLab licenses in order to be able to get stuck into even basic scientific computing).

 

[adfergusson]

Composites must consider: notch sensitivity, bearing-bypass, BVID strength, large notch strength, interlaminar stresses, variety of failure modes/mechanisms, etc.).

Yep, composites are complicated and there are a huge range of physical phenomenae occurring over vastly different length and time scales. It is impossible to incorporate more than a few of these phenomena in any practicable analysis/model. Consequently, experimental testing (and an understanding of how to design and carry out a good experiment) is critical to developing a robust design and modeling methodology. Without good exprimental data to validate against, you'll just end up with some superfluous maths (analytical approach) or Colors For Directors (o.k. That acronym came from CFD but is equally applicable to much of the rubbish FEA work I've seen); neither of which are helpful for designing a real worl product.

To give you an idea of how important I think an understanding of how composites are made and tested is: with the sole exception of my business partner (who is a strategy consultant by background, so I feel this is excusable), everyone in my company can make panels of various composite or bulk resin materials, manually and/or CNC cut a wide range of composite and near resin test specimens from such panels, end-tab them, apply strain gauges/DIC patterns/extensometers, test them, reduce the data, etc... Even then, my business partner can still VARTM a panel and understand some simple scripts even if he doesn't know how to run a test machine or LabView program.

 

[ESPcomposites]

Right. A purely analytical approach is insufficient, but relying on testing exclusively is expensive and limiting. For practical problems, the "trick" is to find the optimal blend of testing and analysis (i.e. semi-empirical approach) for the particular problem. This is more of an engineering problem than an academic problem. Since there are a variety of possible ways to create a semi-empirical method, solutions are often based on prior experience with a history of successful use. Unfortunately, academia doesn't usually explain this very well (if at all). This translates to misleading/confusing information about how to address composites.

Brian

http://www.espcomposites.com

 

[WK95]

Thanks for all the suggestions.

Brian, in your upcoming book, think you can include a little section about composite GA structure in which there are little to no stiffeners but rather a sandwich skin to resist compression and buckling? Us homebuilt aviation enthusiasts would greatly appreciate that.

I ask because you've said elsewhere that your book would be geared towards commercial aircraft but I'd like to know how GA aircraft structures must do things differently. Unfortunately, the literature pertaining to small composite aircraft is substantially more limited that large commercial ones.

 

[adfergusson]

but rather a sandwich skin to resist compression and buckling?

Can't say I have much knowledge of the homebuilt aircraft market and I wasn't aware that sandwich constructions might feature much here; I had (very briefly) once entertained the idea of putting together a Glassair kit many years ago but don't remember it using much in the way of sandwich constructions. Anyway.... Have you looked at literature relating to windturbines? Wind turbine blades make extensive use of sandwich constructions using structural foam cores. Through thickness shear cracking of the core and failure propagating along the profile, but a bit below, the skin-core bond and within the foam are modes of failure that wind turbine blade manufacturers have spend a fair bit of resources looking at and may be relevant to your interests.

 

[berkshire]

Afergusson,
You obviously did not look at the fuselage of the Glassair very much. The fuselage is a foam cored sandwich made in three sections , a left/right and bottom. The attached picture is of one I repaired in 1985 after the aircraft dropped a wheel of the edge of the runway and ground-looped at 40mph.
You can clearly see the construction in the picture.

You are judged not by what you know, but by what you can do.