The linear strain field of the transverse model must be modeled by a series of constant strain elements. The discrepancies can be accounted for by errors in the calculation of frequency from the numerical results. The numerical results should therefore, be exact. The constant strain field of the tensile problems can be modeled exactly by the numerical model. The models dominated by tensile forces (the axially loaded beam and the pressurized ring) were within 0.5% of the theoretical values while the shear dominated model (the transversely loaded beam) is within 5% of the calculated theoretical value. In the model of axial and transverse vibration of a beam and the breathing mode of vibration of a thin ring, the dynamic characteristics were shown more » to be within expected limits. The modeling of dynamic behavior of simple structures was demonstrated within acceptable engineering accuracy. The crack strain field equations are integrated numerically. Except for the crack strain field equations, all terms of the stiffness matrix and load vector are integrated symbolically in Maple V so that fully integrated plane stress and plane strain elements are constructed. The resulting load vector is that of a standard plane element with an additional term that includes the externally applied strain field. The resulting stiffness matrix is that of a standard plane element.
The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed.
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