Are you evaluating homogenised properties or using it ?

Next you question is not clear what you mean to eliminate ?

Normally in HSDT you have to consider displacement function upto third order.

Probably you mean to refer Reddy's Third order shear deformation theory (TSDT).

Thank you sir for helping and Sorry for improper question.

I want to say that :-

1. I want to calculate properties.

2 Eliminate mean when we calculate ABD matrix certain terms gets neglected as done by mondal in using FSDT. So i want in that regard.

3 Yes, i want to use Reddy's theory to evaluate those properties by comparing the properties with effective stiffness.

Did you read literature's on homogenization theory using Higher order theory. It doesn't speak of Reddy's higher theory.

See paper's on higher order theory (HFGMC) for homogenization. You will find article's of Jacob Aboudi, Rami Haji Ali (Parametric HFGMC).

You can go through the book on " Micromechanics of Composite Materials: A Generalized Multiscale " by Brett A. Bednarcyk, Jacob Aboudi, and Steven M. Arnold.

This book might help you immensely on developing the concept of homogenization.