Tensor Analysis With Applications in Mechanics by LEONID LEBEDEVTensor Analysis With Applications in Mechanics by LEONID LEBEDEV

Tensor Analysis With Applications in Mechanics

byLEONID LEBEDEV

Hardcover | May 18, 2010

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The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. This book is a clear, concise, and self-contained treatment of tensors, tensor fields, and their applications. The book contains practically all the material on tensors needed for applications. It shows how this material is applied in mechanics, covering the foundations of the linear theories of elasticity and elastic shells.
Title:Tensor Analysis With Applications in MechanicsFormat:HardcoverDimensions:380 pages, 9.41 × 7.24 × 0.98 inPublished:May 18, 2010Publisher:World Scientific PublishingLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9814313122

ISBN - 13:9789814313124

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