Plane stress and plane strain elements are two-dimensional continuum finite elements used when a three-dimensional body can be idealized by behavior in a representative plane.
How They Work
Plane stress assumes the out-of-plane normal and shear stresses are negligible, which is appropriate for thin plates loaded in their plane. Plane strain assumes the out-of-plane normal strain and shear strains are negligible, which is appropriate for long bodies whose geometry and loading do not vary significantly along the length.
The textbook develops the constant-strain triangular element as the simplest plane element. Each node carries in-plane displacement components, and the element uses a linear displacement field that produces constant strain over the triangle. It then introduces the linear-strain triangle as a higher-order alternative and compares element behavior.
Why It Matters
Plane elements are the first continuum step beyond line elements. They expose key modeling issues that remain important in larger finite element work: element shape quality, stress recovery, compatibility along edges, boundary traction conversion, and convergence under mesh refinement.
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