Finite Element Analysis Assuming Rigid-Ideal-Plastic Material Behavior
- PDF / 1,439,045 Bytes
- 19 Pages / 481.89 x 691.654 pts Page_size
- 10 Downloads / 254 Views
SBN 978-3-7643-0935-0 ISBN 978-3-0348-5891-5 (eBook) DOI 10.1007/978-3-0348-5891-5
FINITE ELEMENT ANAL VSIS ASSUMING RIGID·IDEAL·PLASTIC MATERIAL BEHAVIOR EdoardoAnderheggen Swiss Federal Institute of Technology Institute of Structural Engineering Zürich, Switzerland
ABSTRACT If the material behavior can be adequately described by assuming rigidideal plastic stress-strain-velocity relations the lower- and the upper-bound theorems of the plasticity theory provide powerful tools for the direct determination of limit loads and collapse mechanisms. This approach rElquires the assumption of parametric stress and displacement fields which are constructed by finite element models and leads to the formulation of maximum-minimum problems. If the non-linear,yield conditions are approximated by sets of linear inequalities constraints linear programming can be used to obtain both the ultimate load factor and the shape of the
coll~pse
mechanism. Different finite element
models used for plane stress and plane strain problems are discussed. Some typi ca l numerical results are presented.
NOMENCLATURE c
o E f g h l , j , k. L
m n
NE NJ
material constant defining the yield condition interna 1 rate of energy dissipation coefficient of the equilibrium matrix [E] function defining the yield condition component of body forces index of linearised yield condition (h=1 to Hl coordinate direction indices rate of work. of the external loads index of displacement parameter (m=1 to Ml index 'of stress parameter (n=1 to Nl number of elements number of joints
NS p p q S u V W x a
ß
€ A ~ ~
number of side s between el ements inde x of displacemen t nodal point coeffici ent of the load vec tor {p} i nde x of s t r ess nodal point (q =1 to Q) s t r e ss parame ter di Sp l aceme nt compone nt vol ume of th e body displacement pa r ameter coo rdinate strain ve loci ty fa ctor generali zed str a in veloci ty paramet er s t r a i n component load factor displacement i nt e r po l at i on f unction stress i nt erpo l at i on fun ct ion INTROOUCTION The behavior of comp l ex structural systems above t he e l ast i c range ca n be
determined by elasto-plastic a na l ys i s . This generally requires a stepwise increas e of the external load s a s weIl as some iterations within each load st ep in order to find the new equili bri um conf i gur a t i on. A very different ap proa ch is described i n t hi s pa per: a rigid -ideal -pla s tic mater ial beha vior i s assumed. The lower and upper bound t heorems of the plasti c theory are then us e d to fi nd the col l a ps load, leading to the formula ti on of linear pro grams . The s cope of suc h a n ap proa ch is so meh ow l imited a s t he only i nformations obtained are th e u lti mate l oad f a ct or , the di s t rib uti on of plastic f low dur ing collapse and the sha pe of the colla pse me c hanism . Hoe weve r , the di ffi cu lt ies and t he great comp utat ional e f fo r t usuall y invo l ved in step-by -step elastoplast i c an a lysi s can , t o a l arge e xte nd , be avo ided. The aim o
Data Loading...
