A characterization of families of function sets described by constraints on the gradient
A comparison of homogenization, Hashin-Shtrikman bounds and the Halpin-Tsai equations
In this paper we study a unidirectional and elastic fiber composite. We use the homogenization method to obtain numerical results of the plane strain bulk modulus and the transverse shear modulus. The results are compared with the Hashin-Shtrikman bounds and are found to be close to the lower bounds in both cases. This indicates that the lower bounds might be used as a first approximation of the plane strain bulk modulus and the transverse shear modulus. We also point out the connection with the...
A paradox in the theory of linear elasticity
Let us have the system of partial differential equations of the linear elasticity. We show that the solution of this system with a bounded boundary condition is not generally bounded (i.e., the displacement vector is not bounded). This example is a modification of that given by E. De Giorgi [1].
An approach through orthogonal projections to the study of inhomogeneous or random media with linear response
An inverse problem for biharmonic equation.