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Basic Solid Mechanics
Published in Manoj Kumar Buragohain, Composite Structures, 2017
Small deformation is the one in which the deformed and undeformed configurations of the body are nearly identical. In this case, displacement gradient terms are far smaller than unity, that is, Dij ≪ 1. This class of deformation is governed by the infinitesimal strain theory (also known as small strain theory and small deformation theory), wherein the strain–displacement relations are linear. Deformation characteristics of many engineering materials exhibiting elastic behavior, such as metals and composites, belong to this category. Engineering strains, defined in the previous section are used in the analysis of strains as per the small strain theory.
Triangular and quadrilateral flat shell finite elements for nonlinear analysis of thin-walled reinforced concrete structures in SCAD software
Published in Wojciech Pietraszkiewicz, Wojciech Witkowski, Shell Structures: Theory and Applications Volume 4, 2017
S. Yu. Fialko, V. S. Karpilovskyi
Figure 2 presents the load – displacement diagram in the center of the plate for quadrilateral and triangular finite elements. The mesh 10 × 10 on the quarter part of the plate is considered. The triangular mesh is obtained from quadratic mesh by means of division of each quadrilateral FE into two triangular elements. Twenty divisions across the thickness of the plate are accepted. The increase in the number of divisions across the thickness as well as a refinement of the mesh does not lead to result variation. The deformation theory of plasticity is used.
Solid Mechanics
Published in Eliahu Zahavi, Vladimir Torbilo, Fatigue Design, 2019
Eliahu Zahavi, Vladimir Torbilo
and in the deformation theory it takes the form εijp=32sijσeεp
Mechanical and thermal buckling loads of rectangular FG plates by using higher-order unified formulation
Published in Mechanics of Advanced Materials and Structures, 2021
Mojtaba Farrokh, Majid Afzali, Erasmo Carrera
Different theories for the simulation of the plates have been introduced in the literature so far. In almost all the theories, it is assumed that a midsurface plane can be used to represent the three-dimensional behavior of the plate in two-dimensional form. The oldest theory was developed by Love [16] in 1888 by using the assumptions proposed by Kirchhoff. The Kirchhoff—Love theory is actually an extension of the Euler–Bernoulli beam theory for thin plates. The main assumptions of this theory are that the straight lines normal to the midsurface remain straight and normal to midsurface after deformation. This is also known as the CPT. This theory is only applicable in the thin plate, where the shear effects can be ignored. Numerous plate theories that include shear deformations have been introduced in the literature. The most widely used theory is the first-order shear deformation theory (FSDT). In FSDT, the orthogonality condition of the straight lines to the midsurface after deformation has been relaxed, leading to a constant value of transverse shear strain through the thickness of the plate. There is a discrepancy between the constant state of shear strains in FSDT and the higher-order distribution of shear strains in the elasticity theory. A dimensionless quantity called shear correction factor has been introduced to account for this discrepancy. Different higher-order plate theories have been proposed in order to account for the aforementioned discrepancy. For instance, Reddy [17] has proposed a third-order shear deformation theory (TSDT), whose displacement field accommodates vanishing shear strains at the top and bottom faces of a plate, and it produces parabolic shear strain distribution along the plate thicknesses. Moreover, a general third-order shear theory of the plate has been proposed in which all the displacement fields up to the third-order can be obtained from a unique displacement field [18]. Recently, Carrera et al. has proposed a general higher-order theory that can applicable to plates, shells, and beams [10]. The theory includes a large number of higher-order theories through the CUF.