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    Geometrical solution to static problem without friction

    Homework Statement We have triangle with sides d1,d2,l and angle \alpha between d1 and d2. Assume small change \Delta\alpha of \alpha. Homework Equations Then we can write for \Deltal equation \Deltal=(d1*d2)/(l) * sin\alpha\Delta\alpha. How can I prove that? The Attempt at a...
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    Rate of stress versus velocity gradient

    Hello, I don't understand the meaning of equation \int\dot{s}_{ij}\frac{\partial v_{j}}{\partial x_{i}} dV where \dot{s} is rate of change of stress, v_{j} is velocity. Can anybody describe the meaning of this equation? Thank you.
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    Duality pairing

    Hello all, does anybody know what means duality pairing in connection with functional. For example limE\rightarrow0\frac{\partial}{\partialE}F(u+Ev)=<DF(u),v>. Where F is functional F:K\rightarrowR. Thank You for answers.
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    Core of matrix (pure translatio)

    Hello all, I have problem with name of type of matrix. The definition is next: The core of matrix A is collection of vectors x, for which is valid Ax=0. Does anybody know the name of this type in english language. Example will be also good. Thank You
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    Example from book: continuum mechanics for engineers 2 edition

    example 3.30: Let the stress tensor components σij be derivable from the symmetric tensor field φij by the equation σij = εiqkεjpmφkm,qp. Show that, in the absence of body forces, the equilibrium equations are satisfied. I don't have any idea have to solve this problem. Can someone help...
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    Stress vector

    The stress components in a circular cylinder of length L and radius r are given by sigmaij=[Ay+Bz, Cz, -Cy; Cz, 0, 0; -Cy, 0, 0] (a) Verify that in the absence of body forces the equilibrium equations are satisfied. (b) Show that the stress vector vanishes at all points on the curved...