Questions related to the Continuum Mechanics Division of Elasticity. The bending of beams, deflection of rods, or in general, applications of Hooke's Law generalized to three dimensions.

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3answers
541 views

Consistent theory of continuum

Why is there a consistent theory of continuum mechanics in which one just consider things like differential elements and apply Newtons laws? Is there a deeper reason for it. Is it the nature of ...
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2answers
1k views

Stress tensor in a cube with shear forces

I want to calculate stress matrix in a cube with two faces parallel to x axis and perpendicular to z axis (sorry I don't know how can I put a picture in this post). There are two force uniform ...
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1answer
556 views

Lagrangian density of linear elastic solid

I need the general expression for the lagrangian density of a linear elastic solid. I haven't been able to find this anywhere. Thanks.
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1answer
797 views

Young modulus and Sound Velocity in a continuus medium

In elasticity theory, general equations of motion are: $$\rho \partial^2_t \overline{u} = \mu \nabla^2 \overline{u} + (\mu+\lambda) \nabla(\nabla \cdot \overline{u})$$ where $\overline u$ are ...
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votes
2answers
160 views

Utility of displacements potentials in geophysics

In the elasticity theory, you can derive a wave equation from the fundamental equation of motion for an elastic linear homogeneous isotropic medium: $\rho \partial^2_t \overline{u} = \mu \nabla^2 ...