Shear deformation higher order plate theroies - variational consistent

In summary, shear deformation higher order plate theory is a mathematical model used to describe the behavior of thin plates, taking into account the effects of shear deformation. Variational consistent theories are more accurate and physically meaningful compared to non-variational consistent theories. Higher order plate theories are necessary for accurately capturing plate behavior, especially when the thickness-to-length ratio is small. However, they can be complex and computationally expensive, and may not be applicable to all plate geometries and loading conditions. These theories are validated through comparison with experimental data and more complex finite element simulations, as well as satisfying certain mathematical and physical criteria.
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What is the meaning of...

1. Governing differential equations obtained are consistent with the assumed displacement field (If for a particular theory, governing differential equations are derived using variational approach).

2. Obtained boundary conditions are consistent with the governing differential equations (In case of variational approach is used).


#Shear deformation plate theories
#Higher-order shear deformation plate theories
 
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What is shear deformation higher order plate theory?

Shear deformation higher order plate theory is a mathematical model used to describe the deformation and behavior of thin plates under different loads. It takes into account the effects of shear deformation, which are neglected in classical plate theories.

What is the difference between variational consistent and non-variational consistent higher order plate theories?

Variational consistent higher order plate theories are derived from the principle of virtual work, where the total potential energy of the system is minimized. This leads to a more accurate and physically meaningful solution compared to non-variational consistent theories, which do not follow this principle.

Why do we need higher order plate theories?

Higher order plate theories are necessary to accurately capture the behavior and deformation of thin plates, especially when the thickness-to-length ratio is small. They take into account the effects of shear deformation, which can significantly affect the overall behavior of the plate.

What are the limitations of shear deformation higher order plate theories?

One of the main limitations of shear deformation higher order plate theories is their complexity and computational cost. They require more parameters and variables compared to classical plate theories, making them more difficult to solve and analyze. Additionally, these theories may not be applicable to all types of plate geometries and loading conditions.

How are shear deformation higher order plate theories validated?

Shear deformation higher order plate theories are validated through comparison with experimental data and results from more complex finite element simulations. They should also satisfy certain mathematical and physical criteria, such as energy conservation and stress equilibrium, to ensure their accuracy and reliability.

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