Abstract
STIFFNESS CHARACTERISTICS OF GEOMETRICALLY NON-LINEAR BEAM FINITE ELEMENT/GEOMETRIŠKAI NETIESINIO LENKIAMO STRYPO BAIGTINIO ELEMENTO STANDUMO RODIKLIŲ NUSTATYMAS
Highlights
Two-dimensional geometrically non-linear beam element is considered in this paper
Expressions of geometrically non-linear stiffness matrices are greatly dependent on the introduced assumptions and appropriate elements
Assuming that axial force in the length of element is not constant (the axial force is calculated according to forms (28,29)), the expressions of geometrical stiffness matrix become very complicated
Summary
Visas sistemas modelis yra surenkamas is atskirq elementq naudojant standartinius algoritmus, o geometriskai netiesiniq baigtiniq elementq sistemq analizes ufdavinys yra formuluojamas tik atskiram baigtiniam elementui e. Poslinkis u3 apraSo vidurinio strypo mazgo poslinkj, kurio priklausomybe nuo galiniq mazgq poslinkiq nera tiesine. Vieno is (36) elementq iSraiSka: Suintegravus tiesine standumo matrica atrodo taip:. Pirmasis blokas (2x2) yra ne kas kita, kaip iprasto sarnyrinio-strypinio baigtinio elemento standumo matrica. Gauta taikant kompiuterinct algebrl!, atroda taip (tiesiam elementui): AKWW3(1,1)=3*elea *(2*al**2*ax1 *txl +al**2*tx1 * *2+ 2*al**2*ax2*tx2+al**2*tx2**2-28*al*u1+ 28*al*u2+ 6*al*ax1*wl+ 6*al*ax2*w1+ 6*al*tx1*wl+6*al*tx2*w1 + 24*wl**2-6*al*ax1*w2-6*al*ax2*w2-6*al*tx1*w2-6*al* tx2* w2- 48*wl*w2+24*w2**2+ 6*al*txl*zl+ 6*al*tx2* zl+ 48*wl*zl-48*w2*zl-6*al*txl*z2-6*al* tx2*z2-48*w1* z2+ 48*w2*z2)/ (70*al**3). 4. Netiesinio uzdavinio sprendimo algoritmas Geometriskai netiesines baigtiniq elementq sistemas analizes ufdavinys yra apra8omas netiesinemis algebrinemis lygtimis: kuris apsiribaja deformavimo pracesa nagrinejimu atskiruase zingsniuose, neatliekant iteraciniq skaiciavimq. Del papildomq standumo matricos perskaiciavimq ir biitinumo saugoti dvi sistemas standumo matricas toks metodas reik_alauja daugiau laiko s~naudq bei kompiuterio atminties, taciau apra8o procesus, kurie nepriklauso nuo kreives pobiidzio
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