Page 3 - Demo

Planar Truss Examplefor ComrelAdd-onRCPConsult, 2021-2025Page 3## Global variables to manage plot facilitiesStrurelPlot:=true: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.with(LinearAlgebra):# https://www.maplesoft.com/support/help/maple/view.aspx?path=LinearAlgebrawith(ArrayTools):# https://www.maplesoft.com/support/help/maple/view.aspx?path=ArrayToolsifStrurelPlotthen:with(Maplets[Elements]):# https://www.maplesoft.com/support/help/Maple/view.aspx?path=Maplets/Elementswith(ColorTools):with(plottools):with(plots):endif:PlanarTruss:=proc(INPUT)(*============================================================================Planar Truss Example for Maple============================================================================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 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 @ N04============================================================================*)#### Planar truss model#### Vector input -order from Stochastic ModelA1:=INPUT[1]:A2:=INPUT[2]:E1:=INPUT[3]:E2:=INPUT[4]:p:=INPUT(5..10):# Maple hfarray## 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 :=[[1,13],[1,2],[13,2],[13,12],[2,12],[2,3],[12,3],[12,11],[3,11],[3,4],[11,4],[11,10],[4,10],[4,5],[10,5],[10,9],[5,9],[5,6],[9,6],[9,8],[6,8],[6,7],[8,7]]:## FEM constantsnfe :=upperbound(IEN):# number of barsnnp :=13# number of nodal pointsned :=2# number of dof per nodendof :=ned*nnp:# number of degrees of freedom (dof)## LM: localization matrix, nfe x dof LM :=Matrix(nfe,2*ned):forn tonfe doLM[n,1]:=IEN[n,1]*ned1:LM[n,2]:=IEN[n,1]*ned:LM[n,3]:=IEN[n,2]*ned-1:LM[n,4]:=IEN[n,2]*ned:enddo## Deterministic rod propertiesang :=arctan(200,200):# inclination angle of the truss [deg]theta :=Replicate(Array([ang,0,-ang,0]),6):Remove(theta,-1):# inclination angle [deg]leng :=Replicate(Array(4*[1/sqrt(2),1]),12):Remove(leng,1):# bar length [m]## Stochastic rod propertiesArea :=Replicate(Array([A2,A1]),12):Remove(Area,-1):# bar cross sectional area [m2]E :=Replicate(Array([E2,E1]),12):Remove(E,1):# Young's modulus [N/m^2]## Material propertiesk :=E*Area/leng:# stiffness of each bar## Boundary conditions (supports)cc :=Array([1,2,14]):# dof fixed/supportsdd :=Array(1..ndof,i >i):# dof freeforn fromupperbound(cc)by-1to1dodd :=Remove(dd,cc[n]):enddo## Boundary conditions (applied forces)fc :=Vector(1..ndof):nP :=upperbound(p):forn tonP dofc[14+2*n]:=-p[n]:# negative vertical forces [N]