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During this work, the roof of the car was used as an engineering application to study and monitor the occurrence of failures under the influence of various loads. The shells are made of multilayer composite materials using epoxy resin reinforced with carbon fiber and aluminium oxide granules as reinforcing materials to increase the impact resistance that vehicles may be exposed to while driving, in addition to other loads and conditions such as vibration and constant exposure to moisture and sunlight. The simulation program was used the finite elements method through software Abaqus program in addition to the program MATLAB v.2020a to process the data obtained from the method that used in this study. The results showed that the specified failure criteria work well for predicting the overall structural response such as strain, stress, maximum force and displacement. The losses of energy of impact collision increase as an increase in impact velocity. The dissipation of energy which depend on the stress and strain distribution during elastic deformations. The effect of thickness of the lamina plays an important role in health monitoring the structure. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]