Some exact plane elasticity solutions for nonhomogeneous, orthotropic sheets

Abstract

Exact plane stress solutions are presented for composite material sheets made of parallel fibers embedded in matrix materials. The fibers have variable spacing, and the resulting material is macroscopically orthotropic and nonhomogeneous. Formulas for the variable elastic coefficients are presented for arbitrary fiber spacing. Exact solutions for the stress, strain and displacement fields are presented for four types of problems with arbitrary fiber spacing: (1) Uniform normal stress on the edges parallel to the fibers (i.e., the longitudinal edges), zero normal displacement on the transverse edges; (2) zero normal stress on the longitudinal edges, uniform normal displacement on the transverse edges; (3) zero normal displacement in the longitudinal edges, uniform normal displacement on the transverse edges; and (4) zero normal displacement on the longitudinal edges, uniform shear stress on all edges. For the first three problems, the shear stresses on all boundaries are zero. For the last one, the normal stress on the transverse edge is zero.

Thermal-stress analysis of plates with variable fiber spacing

“…(34) requires γ xy = 0 everywhere. Then, according to a procedure similar to that described in [7], we can immediately show that…”

“…Now, the last question remaining is whether the expression for u in (35) can be integrated in closed form. To this end, assuming V f = 1 − ξ 2 , R 1 = 10, R 2 = 1, ν f = 0.25 and R 4 = 0.08 [7,13], we can derive the following equations: …”

“…The material of such an arrangement can be categorized as orthotropic. When the temperature effect is considered, the stress-strain relationship for an orthotropic sheet under plane-stress condition [1,7] can be written as:…”

“…Almost at the same time, Leissa and Martin [7] got exact solutions for four types of composite sheet problems with arbitrary fiber spacing.…”

Effect of Variable Fiber Spacing on Post-Buckling of Boron/Epoxy Fiber Reinforced Laminated Composite Plate

“…The redistribution may increase the buckling load by as much as 38%. Leissa and Martin also presented exact solutions for the stress, strain and displacement fields for four types of problems with arbitrary fiber spacing [4]. Shiau and Chue also used a similar concept to reduce the free edge interlaminar stresses [5].…”