section (eqn (13)), the vector A is the vector of the transformed node plane deflections defined in the previous section and the vector F is the vector of transformed applied tractions. Suppose for example we consider the three layer system shown in Fig. 4, subjected to surface loading cr..=P(x) when z = 0 (22) q(x) when z = 0 then F = [— Q —P 0000] T where Q=i q(x) dx P = e'xp(x) dx -Suppose for example, the normal load had a triangular distribution {0 p , m ax (a — lxI)/a, 0< < a crzz = elsewhere and the shear distribution was linear {1- max xIa, 0 <Ixl< a 0, elsewhere Then Q =if eq(x) dx itmax i = e x dx a _a 2T

doi:10.1201/9781482286656-21

Chapter

$section (eqn (13)), the vector A is the vector of the transformed node plane deflections defined in the previous section and the vector F is the vector of transformed applied tractions. Suppose for example we consider the three layer system shown in Fig. 4, subjected to surface loading cr..=P(x) when z = 0 (22) q(x) when z = 0 then F = [— Q —P 0000] T where Q=i q(x) dx P = e'xp(x) dx -Suppose for example, the normal load had a triangular distribution {0 p , m ax (a — lxI)/a, 0< < a crzz = elsewhere and the shear distribution was linear {1- max xIa, 0 <Ixl< a 0, elsewhere Then Q =if eq(x) dx itmax i = e x dx a _a 2T$

Chapter

section (eqn (13)), the vector A is the vector of the transformed node plane deflections defined in the previous section and the vector F is the vector of transformed applied tractions. Suppose for example we consider the three layer system shown in Fig. 4, subjected to surface loading cr..=P(x) when z = 0 (22) q(x) when z = 0 then F = [— Q —P 0000] T where Q=i q(x) dx P = e'xp(x) dx -Suppose for example, the normal load had a triangular distribution {0 p , m ax (a — lxI)/a, 0< < a crzz = elsewhere and the shear distribution was linear {1- max xIa, 0 <Ixl< a 0, elsewhere Then Q =if eq(x) dx itmax i = e x dx a _a 2T

ABSTRACT

It will be observed, referring to eqn (21), that both the stiffness matrix K and the load vector F depend upon the integration parameter a, thus eqn (21) determines the vector of node plane displacements as a function of a and so the actual displacements can be evaluated by inverting the transforms using eqn (18). For example suppose we wished to evaluate the displacements on a paticular node plane z = z r,.