4.1.1 Isotropic Elasticity

Table 4.1 summarizes the input data for linear isotropic elasticity for the various structural element families.

Table 4.1: LINEAR ISOTROPIC ELASTICITY

	truss	beam	pl. stress	plate bend.	pl. strain	axisymm.	fl. shell	cu. shell	solid
Young's modulus	E	E	E	E	E	E	E	E	E
Poisson's ratio		$\nu$	$\nu$	$\nu$	$\nu$	$\nu$	$\nu$	$\nu$	$\nu$
Thermal exp.	$\alpha$	$\alpha$	$\alpha$	$\alpha$	$\alpha$	$\alpha$	$\alpha$	$\alpha$	$\alpha$
Concentr. exp.	$\gamma$	$\gamma$	$\gamma$	$\gamma$	$\gamma$	$\gamma$	$\gamma$	$\gamma$	$\gamma$

Note that specification of $\nu$ is not necessary for truss elements. The syntax for the DIANA input data file is as follows.

    (syntax)

YOUNG

e is Young's modulus E . (E > 0 )

POISON

nu is Poisson's ratio $\nu$ . ( 0 $\leq$ $\nu$ < 0.5 )

THERMX

alpha is the thermal expansion coefficient $\alpha$ .

CONCEX

gamma is the concentration expansion coefficient $\gamma$ .

    (file.dat)

'MATERI'
   1  YOUNG  1.2E6
      POISON 0.3

In this example, material 1 may be used for all types of structural elements, provided that the model is not subjected to weight load, temperature load or concentration load.

Position dependency.

For some materials the Young's modulus E may depend on the position of the material in space. A typical example is soil where E may vary with the depth in the soil layer. To model such a dependency, DIANA can apply position dependent characteristics on isotropic elasticity without temperature influence.

DIANA can only handle position dependency for numerically integrated plane stress, plane strain, axisymmetric and solid elements.

    (syntax)

YOUNG

eref is the reference Young's modulus E_ref .

REFPOS

specifies the reference position where xref, yref, and zref respectively are the coordinates ( X_ref, Y_ref, Z_ref ) of the the reference point R for which E_{$\mathsf {R}$} = E_ref .

YNGGRD

specifies the gradient of the Young's modulus in the global XYZ directions: $\partial$E/$\partial$X = grx , $\partial$E/$\partial$Y = gry , $\partial$E/$\partial$Z = grz .

DIANA will calculate the Young's modulus for each element integration point via linear interpolation:

$${\frac{{ \partial E }}{{ \partial X }}} {\frac{{ \partial E }}{{ \partial Y }}} {\frac{{ \partial E }}{{ \partial Z }}}$$ (4.1)

4.1.1.1 Cross-section Analysis

For cross-section elements, used for cross-section analysis [Vol. Analysis Procedures], you must at least specify Young's modulus. Specification of Poisson's ratio or the shear modulus is optional.

    (syntax)

YOUNG

e is Young's modulus E . (E > 0 )

SHRMOD

gxy is the shear modulus G_xy . ( G_xy > 0 )

POISON

nu is Poisson's ratio $\nu$ . ( 0 $\leq$ $\nu$ < 0.5 )