ABSTRACT
Substitutinga'sfromEq.(18-30)intoEq.(18-28)givesthedisplacementfunctionintermsofnodal displacements:
(18-31)
Derivationofstrain-displacementfunction-Thestrain-displacementfunctionEq.(18-21)fora sparelementisreducedtotheform:
(18-32)
Derivationofstress-strainfunction-Thestress-strainrelationshipEq.(18-22)forasparelementis simplifiedbytakingintoaccountthecaseofelasticdeformationofthesparelement,[C]=E.Therefore:
{a}~E{'}~[-11l{:;}(18-33) Derivationofelementstiffnessmatrix-TheelementstiffnessmatrixEq.(18-24)forasparelement
isreducedtotheform: L
[k]~AIr~n[E][ - ~~ldx~AE[1-1]L-11(18-34) 0
Assemblyofalgebraicequations-Asanexample,letusconsidertheassemblyprocedurefora systemthatconsistsoftwospars(Fig.18.12).Letthestiffnessesfortheseelementsbeequaltok 1= A 1E 1 /L 1andk2=A 2E 2/L 2respectively.TheelementmatricescanthenbewrittensimilartoEq. (18-34)inthefollowingform:
81 (18-35)
Fig.18.12Assemblyoftwosparelements.AdaptedfromGinzburg[1].
