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Structural Finite Elements
Published in Michael R. Gosz, Finite Element Method, 2017
Another important assumption in Mindlin-Reissner plate theory is that the normal stress in the Z direction is zero, i.e., σZZ = 0. This assumption does not follow from the kinematic assumptions stated above. We will see later, when we introduce Hooke’s law into the formulation, that assuming σZZ = 0 gives rise to a nonzero extensional strain component in the Z direction. This is in contradiction to equation (7.104), which implies ϵZZ = ∂v/∂Z = 0! Again, such contradictions are common in the development of structural elements. They are justifiable when they simplify the theory and good accuracy is still achieved between the theory and experiment. Note that the assumption σZZ = 0 alone is not identical to the plane-stress assumption discussed in Chapter 4. The plane-stress assumption assumes that the transverse shear stresses, σXZ and σYZ, are also zero. In Mindlin-Reissner plate theory, equation (7.103) allows for the possibility of transverse shear strains, and the associated transverse shear stresses are not ignored.
Brittle damage prediction for corroded stiffened structures under static loading conditions by using peridynamics
Published in Ships and Offshore Structures, 2021
Cong Tien Nguyen, Selda Oterkus
For thin-walled structures, O’Grady and Foster (2014b) developed a PD model for flat shells based on Kirchhoff–Love plate theory. Diyaroglu et al. (2015) developed a PD model for plates based on Mindlin–Reissner plate theory. The PD model developed by Diyaroglu et al. (2015) is later implemented in the finite element framework by Yang et al. (2019). Chowdhury et al. (2016) developed a PD model for curved shell structures by introducing a definition of curve bonds. Recently, Nguyen and Oterkus (2019a) developed a PD model for linear elastic deformations of shell structures in which each shell element has 6 DOFs which can be used to analyse either flat shells, curved shells, or complex shell structures. The PD shell model was also suitable for investigating brittle damages in ship structures (Nguyen and Oterkus 2020). Therefore, this study focuses on predicting progressive brittle damages on corroded stiffened structures by implementing the PD shell model developed by Nguyen and Oterkus (2019a).