By P. Karasudhi (auth.)

This ebook has been written with reasons, as a textbook for engineering classes and as a reference e-book for engineers and scientists. The e-book is an end result of a number of lecture classes. those comprise lectures given to graduate scholars on the Asian Institute of expertise for numerous years, a direction on elasticity for collage of Tokyo graduate scholars within the spring of 1979, and classes on elasticity, viscoelasticity and ftnite deformation on the nationwide collage of Singapore from may perhaps to November 1985. In getting ready this booklet, I saved 3 goals in brain: ftrst, to supply sound primary wisdom of good mechanics within the easiest language attainable; moment, to introduce potent analytical and numerical answer equipment; and 3rd, to provoke on readers that the topic is gorgeous, and is available to these with just a common mathematical historical past. with the intention to meet these pursuits, the ftrst bankruptcy of the booklet is a overview of mathematical foundations meant for somebody whose heritage is an basic wisdom of differential calculus, scalars and vectors, and Newton's legislation of movement. Cartesian tensors are brought rigorously. From then on, simply Cartesian tensors within the indicial notation, with subscript as indices, are used to derive and symbolize all theories.

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Additional info for Foundations of Solid Mechanics

Example text

165 again into the right-hand side of the equation above, while noting its left-hand side is V(

14 Coordinate surfaces and coordinate curves. Mathematical Foundations 37 Fig. 15 Vector dx with components in directions of three coordinate curves. 172) The sets of equations above (Eqs. 172) defme a transformation of coordinates, when the functions involved make the transfoonation admissible and proper. In practice, this assumption may not apply at certain points and special consideration is required. In Fig. 14, the surfaces 01 = Cl> ~ = C2 and 03 = C3 where Cl' C2 and C3 are constants, are called coordinate surfaces.

188b) 2dS~g3 . 188c) "ide1dez At this stage, it is appropriate to introduce two very important contravariant tensors. p. 189) g where g~ is, as defmed in Eq. L of the square matrix [g~. 190b) where a~ is the Kronecker symbol. L=i·g" (1. 192b) g,,' i=g'A· g" =a~ t (1. 192c) is orthogonal to The last equation means physically that a contravariant base vector the coordinate surface eA = constant. Using this property for A. = 1 , we can obtain the area of the side pOsoro of the infmitesimal tetrahedron in Fig.