Based on the Euler beam theory and the elastic strain energy method, the elastic stiffness formula of the holddown spring assembly consisting of several leaves was previously derived. Even though the previous formula was known to be useful to estimate the elastic stiffness of the holddown spring ...
Derivation of mindlin's first and second strain gradient elastic theory via simple lattice and continuum models. Int. J. Solids Struc. 49 (3-4), 470-480.D Polyzos and D I Fotiadis, `Derivation of Mindlin's first and second strain gradient elastic theory via simple lattice and continuum ...
the bar stretches from its original length L0 to a new length Ln. (At the same time, the cross-section decreases.) The stress is defined as the quotient of tensile force divided by cross-sectional area, or F/A. The strain or relative deformation is defined as the difference in length...
Finally, in accordance with stress-strain model derived from the analysis results, as well as diaphragm spring to for instance, the use of the proceeds derived from this variety of materials, and methods of the Model combination using finite element calculation tools, and the load deflection. Tes...
Polyzos and Fotiadis derived the equations of motion of Mindlin's first and second strain gradient elasticity theory by continualizing the response of simple mass-and-spring chains with one-neighbor and two-neighbor interactions in addition to the inclusion of distributed mass alongside lumped mass. ...
and the related rate-of-strain tensor 𝛄˙=(∇𝐯)𝑡+∇𝐯=(∂𝑣𝛼∂𝑥𝛽+∂𝑣𝛽∂𝑥𝛼).γ˙=(∇v)t+∇v=∂vα∂xβ+∂vβ∂xα. (7) 2.2. Free Energy The general form of the free energy of a polymer solution can be written as 𝐴=∫...