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Amirtham Rajagopal's picture

Optimal Nodal Locations in Mesh Free Methods

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  1. How random should be the distribution of nodes in element free galerkin method?
  2. How can we decide if a given nodal distribution is optimal discretization?  In case we are using movin
Mogadalai Gururajan's picture

Some write-ups in mechanics

My googling today brought me to this treasure trove of write-ups in mechanics:

This site contains informal (usually rough draft) technical notes and tutorials on topics in mechanics. The sophistication is at the first or second year graduate level. These write-ups include:

C.H. Wang, "Introduction to Fracture Mechanics"

Here is a link to a 1996 book by C.H. Wang on Fracture Mechanics from the DSTO Aeronautical and Maritime Research Laboratory in Melbourne.



Many of you may know my book on Elasticity, but may not be aware that I also wrote an undergraduate book on Intermediate Mechanics of Materials (Published by McGraw-Hill - ISBN 0-07-232519-4). This picks up from the typical elementary Mechanics of Materials course and deals with the next range of topics such as energy methods, elastic-plastic bending, bending of axisymmetric cylindrical shells and axisymmetric thick-walled cylinders. A full Table of Contents and the Preface are given below.

New graduate mechanics course at MIT: Mechanics of Heterogeneous Materials

16.223 Mechanics of Heterogeneous Materials

Course Description: Mechanical behavior of heterogeneous materials such as thin-film microelectromechanical systems (MEMS) materials and advanced filamentary composites, with particular emphasis on laminated structural configurations. Anisotropic and crystallographic elasticity formulations. Structure, properties and mechanics of constituents such as films, substrates, active materials, fibers, and matrices including nano- and micro-scale constituents. Effective properties from constituent properties. Classical laminated plate theory for modeling structural behavior including extrinsic and intrinsic strains and stresses such as environmental effects. Introduction to buckling of plates and nonlinear (deformations) plate theory. Other issues in modeling heterogeneous materials such as fracture/failure of laminated structures.

John Hutchinson's Notes on Nonlinear Fracture Mechanics (Pages Rotated)

Attached to this post are the notes John posted in his blog, with all pages rotated counterclockwise 90 degrees, for those who would like to read them on their computers.


Notes on Nonlinear Fracture Mechanics

These are the notes I wrote at the Technical University of Denmark in 1979. Zhigang Suo and I will be using these in the course on fracture and thin film mechanics (ES 242r) this spring (2007). This is a joint course with the University of Nebraska.

Engineering Sciences 242r: Fracture Mechanics of Thin Films and Composite Materials

Time. Thursday and Tuesday. 1:30-3:00 pm (Harvard University), 12:30-2:2:00 pm (University of Nebraska). First meeting: 1 February 2007

Place. Harvard University: Fairchild 102 (map). University of Nebraska: 111 Walter Scott Engineering Center

Course website (this page): node/754

discontinuities in mesh free methods

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I wish to ask where to find literature about introducing discontinuities in the shape functions to simulate cracks in mesh free methods.

I found the visibility criterion, the diffraction method and the transparency method referred in the (I think vey good) survey by Fries and Matthies "classification and overview of meshdree methods" but nothing else.

thank you,

project from solid mechanics

dear mechanicians,

i am student of btech 2nd year,mechanical from iit roorkee.i am looking forward for doing project work in solid mechanics.i know it's a vast topic and thats why i want your help in guiding me.i have not had this as a subject till now so i am confused about ani idea of project work.please give me some details as to where to start with.very thanks.

Zhigang Suo's picture

Engineering Sciences 241: Advanced Elasticity

This is a second graduate course in solid mechanics.  Building on thermodynamics and linear algebra, the course explores coupled mechanical, thermal, electrical, and chemical actions.  The course draws heavily upon phenomena in soft active materials.

This page is updated for ES 241 taught in Fall 2017 (See also Google doc for lecture-by-lecture record and homework)

The course taught in the past:

MichelleLOyen's picture

Introductory Biomechanics Courses

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In the early days of biomechanics, there probably were not many dedicated biomechanics courses and instead a regular mechanics curriculum was studied by people interested in tissues and biosystems. However, now that there are so many dedicated bioengineering programs at Universities throughout the world, it seems as though it is more likely that much of students' basic mechanics knowledge comes through dedicated biomechanics courses. This then in turn raises the interesting question of what is taught in these courses?

Mogadalai Gururajan's picture

The SIAM 100-digit challenge of Bronemann et al: A review

Suppose if somebody asked you the following question, and more importantly, wanted the answer to an accuracy of 100-digits:

  • Problem A: A particle at the center of a 10 x 1 rectangle undergoes Brownian motion (i.e., two-dimensional random walk with infinitesimal step lengths) until it hits the boundary. What is the probability that it hits at one of the ends rather than at one of the sides?

Or, this question (again, demanding the answer to an accuracy of 100-digits):

MichelleLOyen's picture

J-Club participation: advice for students

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Now that the Journal Club is getting started, I wanted to post some advice for students who may not have participated in such a forum in the past, either online or in person. The fun of a J-club includes the opportunity to broaden your understanding of the literature of a broad field (like mechanics) by reading carefully-selected groups of papers on small topics of interest to different sub-communities. The challenge in participating in the subsequent discussion is ensuring that you understand the papers sufficiently to participate confidently in the ensuing discussion. This will also prepare you to be a good reviewer for technical journals some day.

The Energy Blog

I just jointed iMechanica. Great blog site! I thought to bring to your attention another blog that I enjoy, run by a retired engineer, on renewable energy issues. Here is the link:

Pure shear decomposition of the deformation gradient for finite strain measures


I am wondering about deformation gradient for pure shear decompositions. As i saw much literature on simple shear, I couldn't able to track one on pure shear.

Please some one in this forum provide me with literaure and fine details.





MichelleLOyen's picture

New Book "Tissue Mechanics"

A new book, "Tissue Mechanics" by SC Cowin and SB Doty is of potential interest to those from a classical mechanics background considering work in biomechanics. Downloadable versions of the first two chapters are available at the book's website along with a full table of contents and other supplemental information.

Adrian Podpirka's picture

MEMS Doubly Clamped High Sensitivity Mass Detector

After reading the abstract on the resonanting cantilever mass detector, I think this paper might be of interest to some.  My colleagues and I wrote this for a MEMS device class we took Fall 2005 at Columbia University while I was an undergraduate.  It was a term design project.

Abstract – Micro-electromechanical systems (MEMS) often provide cost effective 

Master of Science in Mechatronic Systems Engineering

Lawrence Technological University has introduced a new master’s degree program in mechatronic systems engineering, a philosophical approach that cuts across multiple scientific disciplines.

Mechatronic systems engineers design enhanced products, systems and manufacturing processes by bringing together knowledge from mechanical engineering, electrical engineering and computer science. Students learn new principles for designing mechanical subsystems to satisfy control requirements.

EFG Matlab Routines

These used to be hosted at Northwestern, but the files were taken down some time ago. The original 1d and 2d Matlab routines for the element-free Galerkin method are now located at

These routines are described in detail in the paper

J. Dolbow and T. Belytschko (1998), "An Introduction to Programming the Meshless Element Free Galerkin Method," Archives of Computational Methods in Engineering, vol. 5, no. 3, pp. 207--242.


I am writing to you to bring to your attention a new Master Course on Computational Mechanics, which has been awarded the Erasmus Mundus label.

It is an international Master course given jointly in English by the Universidad Politécnica de Cataluña (Barcelona), University of Wales Swansea), Ecole Centrale Nantes and Universität Stuttgart with the collaboration of CIMNE International Centre for Numerical Methods in Engineering, Barcelona). The Erasmus Mundus program:

Mechanical Properties of Thin Films (class notes for a graduate class at Stanford University)

The attached file is a set of class notes developed by W.D. Nix of Stanford University and used in a graduate course on Mechanical Properties of Thin Films. These notes have been used in the graduate course MSE 353 since the late 1980's. That course has been taught every year or so since that time. The notes were last updated in January of 2005. The reader will see a note to the effect that many of the figures and illustrations in the file have been taken from the work of students and colleagues at Stanford without proper attribution.


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