The common damage in engineering structures, especially in functionally graded materials, such as failure resulting from fiber breaking or cracking in the matrix or deboning between fibers and matrix, as well as the delamination between the composite material plies and between its layers, may be due to thermal effects, vibration, load concentration as a result of stress and strain for provides information’s about structural health monitoring. Virtual energy method such as Hamilton's was used to investigate the effect of the design parameters such as side to thickness and modular as well as material graduation index ratio on the stress-strain relationships, displacement, resultants of stresses, and resultants of mid plane strain. The analysis and simulation of the FGM shells is done in this paper utilizing MATLAB19 code and ABAQUS20 programs. The distribution of characteristics across shell thickness had also been determined using a power law. Normal stress was varied gradually from 5.74 MPa to 9.55 MPa with material index (n) from 0 to 10 respectively, while shear stress varied from 4.2 to 8.23 MPa for the same value of (n). The strain percent increased slightly from 0.00059 to 0.0012 with displacement 0.22 and 1.2 respectively for the same value of (n).
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