Page 3 - Demo

Planar TrussExamplefor ComrelAdd-onRCPConsult, 2022-2025Page 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.globalStrurelPlotNameStrurelPlotTypeStrurelPlotModeStrurelPlotCountfunctionlsfval=PlanarTruss(XP)/*============================================================================Planar Truss Example for Scilab============================================================================Inputs:X = [A1, A2, E1, E2, P1, P2, P3, P4, P5, P6, u_y]E1,E2: Youngs modulus of horizontal and inclined bars resp. lognormally distributedA1,A2: cross section of horizontal and inclined bars resp. lognormally distributedP1P6: negative vertical forces attacking in nodes 813. 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 @ N04============================================================================*///!//! Planar truss model//!---------------------------------------------------------------------------//! Global variables to manage plot facilitiesStrurelPlot=%tglobalStrurelPlotNameStrurelPlotTypeStrurelPlotModeStrurelPlotCountStrurelPlotName='PlanarTruss_';StrurelPlotType='.png';StrurelPlotMode=int32(3)//! 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)//! Element, 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 dof LM =cell(nfe,1);fore =1:nfeLM{e}=[IEN(e,1)*ned1,IEN(e,1)*ned,IEN(e,2)*ned1,IEN(e,2)*ned];// element 1 has dof 12 & 2526 ...end//! 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]theta =repmat([ang 0-ang 0],1,ng/2);theta($)=[];// inclination angle [deg]leng =repmat(4*[1/sqrt(2)1],1,ng);leng($)=[];// bar length [m]//! Stochastic rod propertiesArea =repmat([A2A1],1,ng);Area($)=[];// bar cross sectional area [m2]E =repmat([E2E1],1,ng);E($)=[];// Young's modulus [N/m^2]//! Material propertiesk =E.*Area./leng;// stiffness of each bar//! Stiffness matrix assemblyK =zeros(ndof,ndof);// stiffness matrixT =cell(nfe,1);// transformation matrixfore =1:nfe // sin and cos of the inclinationc =cos(theta(e));s =sin(theta(e));// coordinate transformation matrix for the bar eT{e}=[c s 00;-s c 00;00c s;00-s c ];// local stiffness matrix for the bar e Kloc =k(e)*[1010;0000;-1010;0000];// global stiffness matrix assemblyK(LM{e},LM{e})=K(LM{e},LM{e})+T{e}'*Kloc*T{e};end//! Boundary conditions// Applied loadsfc =zeros(ndof,1);fc(16:226)=P;// negative vertical forces [N]// Supports and free nodesc =[1214];// fixed dofs