Uniqueness Theorems in Linear Elasticity by Robin J. Knops, L. E. Payne


Uniqueness Theorems in Linear Elasticity by Robin J. Knops, L. E. Payne

The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniqueness in elasticity theory in the hope that such an exposition will provide a convenient access to the literature while at the same time indicating what progress has been made and what problems still await solution. Naturally, the continuing announcement of new results thwarts any attempt to provide a complete assessment. Apart from linear elasticity theory itself, there are several other areas where elastic uniqueness is significant.

About the Author

Other Formats

Book Info


142 pages


Robin J. Knops, L. E. Payne
More books by Robin J. Knops, L. E. Payne



Publication date

1st January 1971



I love finding new books to read. My mummy and me look at the new ones coming out. I have written reviews of some of them!

Jessica Cobbin – age 7

It’s really exciting to read and review new books, thrilling to see my reviews online and I love finding the final published copies on sale.

Sam Harper – age 10

It gives me a chance to read types of books that I would not normally try, and it motivates me to read every night to finish it!

Alice Horncastle, age 14

This company is amazing; not only is it is a great opportunity to get books and review them but everyone is so friendly and supportive!

Jemma Rubens, age 10

Lovereading is just a convenient way to find new books and hear others opinions on them.

Sarah Murray – age 15

I love ‘LoveReading 4 kids’ because they let you read and learn things you’d never dreamed of learning before.

Emily Horncastle – age 11

It is THE website to use for narrowing down your search for any book. Definitely knocks the socks off any other book review website.

Nickey and Tomasz Hawryszczuk

At @HHSHaringey we love @lovereading4kids because our pupils can practice reviewing & get free upcoming books before anyone else!

Helen Swinyard – Heartlands High

Lovereading 4 schools