23.9 : 三维应变分析

Three-dimensional strain analysis uses principal stress axes to evaluate deformation in elastic, homogeneous materials.

A small cubic element, when expanded around these axes, transforms into a rectangular parallelepiped, illustrating the deformation.

The strain analysis involves rotating an element around a principal axis, like the n-axis, and evaluating strain components on faces perpendicular to this axis. This method is based on plane strain transformation.

Using Mohr's circle, strain transformation is examined as the cube rotates around principal axes. This approach identifies the maximum shearing strain at a certain point, equivalent to the diameter of the largest of the three circles.

In plane strain, the n-axis transforms into a principal axis with zero strain at the origin of Mohr's circle diagram. Principal strains on opposite sides of this origin represent the maximum and minimum normal strains.

In thin plates of structures experiencing plane stress, the n-axis turns into a principal stress axis.

The principal strain along the n-axis is associated with in-plane strains. Rotation about the m-axis defines maximum shearing strain.