In this article, a mathematical model for beams with partially delaminated layers is presented to investigate their behavior by using Euler-Bernoulli beam theory. The principal advantage of the element is that it allows the modeling of delamination anywhere in the structure. The region without delamination is modeled to carry constant peel and shear stresses; while the region with delamination is modeled by assuming that there is no peel and shear stress transfer between the top and bottom layers. Moreover, in the interfaces between the regions with and without delamination, both displacements and forces continuity conditions are imposed. The accuracy of the models is verified by comparing results with previously published data.

In this paper, a mathematical model for beams with partially delaminated layers is presented to investigate their behavior. In this formulation account is taken of lateral strains. The principal advantage of the element is that it allows the modeling of delamination anywhere in the structure. Numerical results of the present model are presented and its performance is evaluated for static problems.

A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.

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