Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events. In this paper we prove an inclusion-exclusion principle for IF-STATES based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events. Finally, we give some applications of this principle by extending some results regarding the classical probabilities to the case of the IF-STATES.

Despite the definition of failure being almost thoroughly studied in other theories such as elasto-plasticity, this paper studies the possibility of capturing or defining some LIMIT STATES in hypoelastic materials. It is shown that for many hypoelastic materials the LIMIT state, as a notion of failure, can take the place of the yield or failure in classical plasticity. The procedure is general, and all equations are rational, i.e. they are not dependent on a particular form of a constitutive equation. Constitutive equations cover those applied to both metallic and non-metallic materials. Some practical results were obtained for a particular form of a hypoelastic equation which resembles the Drucker-Prager criterion for the form of the LIMIT state. Results were also examined against a set of experimental data.

Fragility curve, based on the performance-based earthquake engineering (PBEE), is a fundamental tool in assessing the probabilistic seismic performance of concrete gravity dams. Determination of the dam LIMIT-STATES (LSs) is necessary for estimation of fragility curve. In this research, four LSs in seismic performance of massive structure have been utilized for Pine Flat dam. To address this, the Incremental Dynamic Analysis (IDA) method has been applied to the integrated dam-reservoir finite-element model. Evaluation of seismic behavior, demand and capacity of the tallest monolith has been investigated by implementing IDA. A new comprehensive method in terms of IDA and statistical analysis has been used for determination of each defined LS based on the certain value of the engineering demand parameter (EDP). To assess probabilistic performance of the dam, the exceeding probability of the LSs curves has been developed at various intensity measures based on the tree EDPs. It was found that the defined LSs have the capability indeed to be used in probabilistic framework.

In this Study، according to microfluidic structure and bio inspired techniques، a material detection sensor has been DESIGNed and fabricated based on micro fabrication method. The capacitive sensing has been DESIGNed numerically and optimized by a familiar multi physics software. In this type of sensor، a defined aptamer has been coated on the capacitor electrode surface and by flowing the fluid through the microchannel، the targeted material would be involved between the aptamer string structure and it makes a change in capacitor value. In this research، a novel readout system based on LIMIT cycle has been introduced and implemented. In this method، a virtual nonlinear dynamic has been supposed beside the real system and makes the whole system behave in a LIMIT cycle (LC). By measuring LC frequency and amplitude، capacitor value is estimated.