^{0}, 90^{0}, 0^{0}/90^{0}/0^{0} respectively with aspect ratio 20. In accordance with this we observed uniformity among the predicted values.

In recent years, the concept of calculation of transverse deformation changed from a functionally graded material to composite materials that integrates the thermal components in the beam

From the above findings, it is investigated that the existing solution for simply supported beam having uniformly distributed load with thermal load can be improved through, the developing a solution that can solve using von Kármán mathematical non linearity, supposition and Boltzmann constitutive connection, dual mesh control domain methods, Kirchhoff’s theory, Reuss model, the Voigt model, the Mori-Tanaka model, Hashin-Shtrikman bound model Euler-Bernoulli equation, elementary beam theory (ETB), first order sheared formation theory (FSDT), higher order shear deformation theories (HSDT) and trigonometric shear deformation theory (TSDT). To achieve these possible improvements, the researcher developed a Navier solution.

This presents a detailed discussion of the methods, techniques, and tools the researchers used to satisfy the identified objectives. The hyperbolic shear deformation theory (HYSDT) gives exact solution for simply supported beam with thermal load using Navier equation. MATLAB code used for mathematical equation to find transvers displacement.

Epoxy resins is the material which is used in present theory. Epoxy resins are mostly used in aerospace structures for high performance applications. The displacement field of the present composite laminated beam theory can be expressed as follows:

Where u is the displacement in the x direction and w is transverse displacement in the y direction of a point on the beam in mid plane. The temperature distribution across the thickness of laminated beam is assumed to be in the form as given below

In the above equation, T is the temperature change from a reference state which is a function of x and z. The thermal load T_{0} is linearly varying across the thickness of laminated beam is a function of x.

For 0

For 90

For

Present HYSDT 4.912 0.851 9.951 1.711 0.369 3.468 TSDT 4.160 0.734 9.045 1.460 0.340 3.022 HSDT 5.055 0.849 10.562 1.730 0.369 3.533 FSDT 0.226 0.261 0.462 0.208 0.217 0.437 ETB 0.202 0.203 0.429 0.202 0.203 0.429
Present HYSDT 0.465 0.230 0.965 0.269 0.210 0.562 TSDT 0.420 0.225 0.869 0.258 0.210 0.540 HSDT 4.466 0.230 0.960 0.269 0208 0.563 FSDT 0.203 0.205 0.430 0.202 0.210 0.429 ETB 0.202 0.203 0.429 0.202 0.203 0.429

^{0}
^{0}
^{0}/90^{0}/0^{0}
^{0}
^{0}
^{0}/90^{0}/0^{0}

^{0}
^{0}
^{0}/90^{0}/0^{0}
^{0}
^{0}
^{0}/90^{0}/0^{0}

The researcher performed analysis of simply supported beam with uniformly distributed load along with thermal load. The researcher has applied virtual work method and had developed governing differential equations in accordance with the hyperbolic shear deformation theory to satisfy the transverse displacement outcome. The Prime focus was to consider transverse displacement in order to satisfy the considerations of Navier’s theory and thus exhibiting variable angle ply patterns by satisfying the needs of beam analysis. This systematic exposition of theory gives exact solution to simply supported beam analysis as compared to elementary beam theory (ETB), first order sheared formation theory (FSDT), higher order shear deformation theories (HSDT) and trigonometric shear deformation theory (TSDT).

In accordance with the result, we achieved for finding exact solution to the simply supported beam analysis by using Navier’s theory, hyperbolic shear deformation theory (HYSDT) in comparison to first order sheared formation theory (FSDT), higher order shear deformation theories (HSDT) and trigonometric shear deformation theory (TSDT). We achieved exact solution of transverse displacement for different ply angles such as 00, 900 and 00/900/00. Convergence studies carried out for the transverse displacement of symmetric cross-ply beams showed significant variations among ETB, FSDT, HDST and TSDT with aspect ratio 2,4,10 and are tabulated in

The thermal response of single layer orthotropic, two-layer antisymmetric, and three-layer symmetric cross ply laminated beams subjected to pure thermal load for varied aspect ratios has been investigated using a computational model based on sinusoidal shear deformation theory. The transverse deformation, which is particularly critical in thick beams, is given special consideration. For laminated composite beams, a novel hyperbolic higher order shear deformation theory is provided. Because the theory accounts for proper transverse displacement distribution across the beam thickness, no shear correction factor is necessary. Classical beam theory, first-order shear deformation theory, and higher-order shear deformation theory are all used to compare the results. Under evenly distributed thermal load, the conclusions of the present theory match well with those of higher-order shear deformation theory. Except for ETB, when a symmetric cross-ply laminated beam is subjected to evenly distributed thermal load, transverse displacement changes as the aspect ratio changes from 2 to 20.