A formulation for vibration analysis of beams based on reference-plane formulation is proposed.
Conventional beam elements based on the mid-plane formulation are often used to predict vibration frequencies of beams.
A complete solution to the contact problem, within the context of an elastic half-plane formulation, is derived, including the effects of a shearing force either sufficient or insufficient to cause sliding.
Vibration frequencies predicted from the proposed reference-plane formulation were shown to agree well with the results from FE models based on generalized beam elements, composite shell elements, and 3D solid elements.
Recently published work on the vibration of functionally graded materials (FGM) beams shows that if the positions of immovable end supports are at a different plane to the middle-plane, beam elements based on mid-plane formulation will yield inaccurate results.
A dynamic boundary-value problem in a plane strain formulation is solved numerically by the finite-difference method.
The paper addresses wave motions in an unbounded sandwich plate with and without heavy fluid loading in a plane problem formulation.
Although there exists an extensive literature on 3-D solution of this problem, a simplified non-isentropic plane wave formulation is not seen.
This paper addresses analysis of wave motions in an unbounded sandwich plate with and without heavy fluid loading in the plane problem formulation.
Among these examples, a plane stress formulation is described in more detail, namely, Yld2000-2d [Barlat, F., Brem, J.C., Yoon, J.W., Dick, R.E., Choi, S.H., Chung, K., Lege, D.J., 2000. Constitutive modeling for aluminum sheet forming simulations.
