Theories are presented for rods and plates consisting of a porous elastic medium saturated with a fluid, for which the flow is possible in the longitudinal direction(s) only, as a result of the microgeometry of the solid skeletal material. Biot's constitutive equations are employed and Darcy's law is adopted for describing the relative motion between the solid and fluid. The drained medium is taken to be elastic and transversely isotropic, i.e. isotropic in the cross section of the rod or in the plane of the plate. Both small deflection and large deflection formulations are derived for the case of rods. For plate the Kirchhoff hypotheses are adopted and thus a linear theory is presented. Analytical solutions of the linear theories are found for quasistatic and vibration problems of beams and plates, as well as for buckling of columns. In addition, a mixed finite element scheme is developed for the quasistatic rods with small deflection, in order to solve problems with general loading and boundary conditions. Variational principles are first established for this purpose. For large deflection of the beams solutions are obtained by using the finite difference method.

For vibrations the mechanical system is found to be characterized by three time scales, which are defined by the material and the geometry of the structural element. Observations are made concerning the various solutions obtained, and the unique time dependent behaviours of such elements are pointed out.

The present work could help understand the response of plant elements or the like to loads and possibly provide a theoretical basis for damage control of such structures in situations of buckling or vibrations. The results also show the possibility of converting such elements, ideally made of artificial materials of the type investigated, into smart structures.