Page 3 - Demo

Planar TrussExamplefor ComrelAdd-onRCPConsult, 2022-2025Page 3//! Global flags to manage plot facilitiesStrurelPlot=1;StrurelPlotName=\_\StrurelPlotType=\StrurelPlotMode=3;//! Code based on Max Ehre work https://github.com/maxehre/polynomial_surrogates//! Used with his kind permission as version from 2017 that adapted to Strurel.procPlanarTruss(XP);/*============================================================================Planar Truss Example for Gauss============================================================================Inputs:X = [A1, A2, E1, E2, P1, P2, P3, P4, P5, P6, u_y]E1,E2: Youngs modulus of horizontal and inclined bars resp. -log-normally distributedA1,A2: cross section of horizontal and inclined bars resp. -log-normally distributedP1-P6: negative vertical forces attacking in nodes 8-13. -Gumbel distributedu_y: maximal allowed vertical deflection in node 4. constantOutput:uout: vertical truss deflection at bottom center (N04)============================================================================Truss description taken from Lee, S.H., Kwak, B.M. (2006).Response surface augmented moment method for efficient reliability analysis.Structural Safety 28(3), 261 272.https://www.sciencedirect.com/science/article/abs/pii/S0167473005000421Based on Diego Andr%u00e9s Alvarez Mar%u00edn work https://github.com/diegoandresalvarez/elementosfinitos/tree/master/codigo/repaso_matricial/cercha_2dN: NodesR: Rods============================================================================N13__R4___N12__R8___N11__R12__N10__R16__N09__R20__N08/\\/\\/\\/\\/\\/\\/ \\/ \\/ \\/ \\/ \\/ \\R1 R3 R5 R7 R9 R11 R13 R15 R17 R19 R21 R23/ \\/ \\/ \\/ \\/ \\/ \\/___R2___\\/___R6___\\/__R10___\\/__R14___\\/__R18___\\/__R22___\\N01 N02 N03 N04 N05 N06 N07||\\/uout => u_y============================================================================*///!---------------------------------------------------------------------------//! Planar truss model//!//! All local variables inside of procedurelocalA1,A2,E1,E2,P,nfe,ned,nnp,ndof,IEN,LM,Grid,ng,ang,t1,theta,l1,leng,Area,E,ke,K,co,si,Tb,T,TD,Kloc,fc,c,d,Kcc,Kcd,Kdc,Kdd,ac,ad,qd,a,q,NEL,TT,uout,tit,XY,b,DF,x,y,n,fd,l,X,Y,Xrot,Yrot,xo,xe,yo,ye,ll,cc,ww,tt,cn,minA,maxA,dA,Su,q;//! Vector inputs order from Stochastic ModelA1=XP[1];// cross section of horizontal barsA2=XP[2];// cross section of inclined barsE1=XP[3];// Youngs modulus of horizontal barsE2=XP[4];// Youngs modulus of inclined barsP=XP[5:10];// negative vertical forces attacking in nodes 813. (1x6 vector)//! Initial input variablesnfe =23;// number of elements (bars)ned =2;// number of dof per nodennp =13;// number of nodal pointsndof =ned*nnp;// number of degrees of freedom (dof)//! Elements, nodes and dofs association//! IEN: connectivity matrix, nfe x nodes bar 1 has nodes 1 and 13, bar 2 has nodes 1 and 2 ...IEN ={113,12,132,1312,212,23,123,1211,311,34,114,1110,410,45,105,109,59,56,96,98,68,67,87};//! LM: localization matrix, nfe x dofLM =zeros(nfe,2*ned);forn (1,nfe,1);LM[n,1]=IEN[n,1]*ned1;LM[n,2]=IEN[n,1]*ned;// element 1 has dof 12 & 2526 ...LM[n,3]=IEN[n,2]*ned1;LM[n,4]=IEN[n,2]*ned;endfor;//! Deterministic rod propertiesGrid =4;// size of grid side in [m]ng =12;// count of grid cellsang =atan(Grid/Grid);// inclination angle of the truss [deg]t1={10-10};t1=t1*ang;forn (1,ng/2,1);theta=t1 |t1;endfor;theta=reshape(theta,1,ng*2);// inclination angle [deg]theta=delcols(theta,1);l1={00};l1[1]=Grid/sqrt(2);l1[2]=Grid;forn (1,ng,1);leng=l1 |l1;endfor;leng=reshape(leng,1,ng*2);// bar length [m]leng=delcols(leng,1);//! Stochastic rod propertiesArea=zeros(1,ng*2);forn (1,ng*2,2);Area[n ]=A2;Area[n+1]=A1;// bar cross sectional area [m2]endfor;Area=delcols(Area,1);E=zeros(1,ng*2);forn (1,ng*2,2);E[n ]=E2;E[n+1]=E1;// Young's modulus [N/m^2]endfor;E=delcols(E,1);//! Material propertieske =E.*Area./leng;// stiffness of each bar//! Stiffness matrix assemblyK =zeros(ndof,ndof);// stiffness matrixTb=arrayinit(nfe |4|4,0);// coordinate transformation matrix for the bar nTD ={1010,// transformaion matrix0000,