The study of the validity and probability of failure in solids and structures is highly considered as one of the most incredibly-highlighted study fields in many science and engineering applications, the design analysts must therefore seek to investigate the points where the failing strains may be occurred, the probabilities of which these strains can cause the existing cracks to propagate through the fractured medium considered, and thereafter the solutions by which the analysts can adopt the approachable techniques to reduce/arrest these propagating cracks.In the present study a theoretical investigation upon simply-supported thin plates having surface cracks within their structure is to be accomplished, and the applied impact load to these thin plates tends to induce almost infinite strains nearby the crack tip of the existing cracks. The distribution of these strains and the probability distribution of failure due to these strains are to be of a particular importance within the current research.Within the current study a modified theoretical technique, which is derived from the classical plate theory, whose concepts are illustrating the required plane-stress conditions for fractured thin plates, taking into consideration the impact-load effects in conjunction with the fracture-mechanics concepts, is to be followed and obeyed so as to arrive at the required equations representing the nearby-tip strains within the thin plates made from the pure aluminum 1100 type alloys. A further statistically-based analysis must lead into the utilization of the joint probability distributions having two random variables in order to construct the required probability distributions of the failure which may be occurred due to the highly-localized nearby-tip strains.
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