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# Computation of Three Dimensional Stresses Based on ESL Theory

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## Results are presented for a

Results are presented for a simply supported laminated composite beams under transverse sinusoidal load applied at the top surface of the beam. The transverse shear stress is computed without imposing continuity condition in the formulatio a priori and constitutive law. The transverse normal stress is cmputed using constitutive law. The trandverse shear stress is computed with about 5% for yhin and moderately thick beams. For thick beam it is about 6% at the interfaces.

The trandverse normal stresss is also computed with the above trend

## Computation of Three

Computation of Three Dimensional Stresses Based on the concept of ESL Theory

A new method has been used to accurately compute three dimensional stresses without using equilibrium equations.

There are three ways to accurately calculate transverse normal and shear stresses: The New method, Constitutive law and integration of equilibrium method. This research work uses only the new method and constitutive law.

In this formulation, the continuity conditions of transverse stresses are not imposed at the layer interfaces a priori. There are no additional requirements of computational effort. Further number of unknowns is not increased because of ESL theory.

The transverse shear stress can accurately be calculated only from this new method and the results from the constitutive law are not at all satisfactory . This method gives continuity at the layer interfaces.

The transverse normal stress is calculated either from the new method or constitutive law in this research work. The new method gives continuous transverse normal stress at the layer interfaces whereas computation from the constitutive law gives discontinuous normal stress at the layer interfaces.

The results for thin and moderately thick beams are excellent. Though the accuracy decreases for thick beams (aspect ratio 5), the values of the stresses at the layer interfaces are accurately predicted.

This research work shows that three dimensional stresses can accurately be calculated from two dimensional theory (ies).

## Computation of Three

Computation of Three Dimensional Stresses Based on the concept of ESL Theory

A new method has been used to accurately compute three dimensional stresses without using equilibrium equations.

There are three ways to accurately calculate transverse normal and shear stresses: The New method, Constitutive law and integration of equilibrium method. This research work uses only the new method and constitutive law.

In this formulation, the continuity conditions of transverse stresses are not imposed at the layer interfaces a priori. There are no additional requirements of computational effort. Further number of unknowns is not increased because of ESL theory.

The transverse shear stress can accurately be calculated only from this new method and the results from the constitutive law are not at all satisfactory . This method gives continuity at the layer interfaces.

The transverse normal stress is calculated either from the new method or constitutive law in this research work. The new method gives continuous transverse normal stress at the layer interfaces whereas computation from the constitutive law gives discontinuous normal stress at the layer interfaces.

The results for thin and moderately thick beams are excellent. Though the accuracy decreases for thick beams (aspect ratio 5), the values of the stresses at the layer interfaces are accurately predicted.

This research work shows that three dimensional stresses can accurately be calculated from two dimensional theory (ies).