FEMStress.2d {FEA}

FEMStress.2d

Description

Creates a complete finite element model using stress for a given 2D mesh under specified boundary conditions (constrain and load).

Usage

FEMStress.2d(meshP, meshT, centroid, BoundConx, BoundCony, SFShear,
SFTensile, Length, area, Fx, Fy,  Y, Nu, Thick)

Arguments

meshP

Matrix (2 x n) containing coordinate points of the mesh nodes.

meshT

Matrix (3 x n) containing the number of the coordinate point that forms a given triangle within the mesh.

centroid

Matrix (2 x n) containing coordinate points of the centroid of each triangular element.

BoundConx

Boundary constraint for nodes in the x-direction

BoundCony

Boundary constraint for nodes in the y-direction

SFShear

Magnitude of positive shear traction; if there is no surface traction then SFShear = 0

SFTensile

Magnitude of tensile surface traction; if there is no surface traction then SFTensile = 0

Length

Truss length

area

Triangle element area

Fx

Load vector for the x-direction

Fy

Load vector for the y-direction

Y

Value of Young's (Elastic) modulus

Nu

Value of Poisson's ratio

Thick

Value of the thickness of the mesh, a value must be given.

Value

Completes the FEM to generate values of stress and strain and nodal displacement.

NodeDisplacement

Node displacement on each axis

LocalStress

Stress as calucated from stress, strain, and stress from strain. Three (3) [3 x n] matrices where [x, y, tau]

Examples

data(triMesh)
data(dime)

meshP = triMesh$MeshPts$p
meshT = triMesh$MeshPts$T
centroid = triMesh$Centroids
Y = matrix(20e9, nrow = NROW(meshT))
Nu = matrix(0.45, nrow = NROW(meshT))
Thick = 0.001
DOF = 6
BoundConx = BoundCony = numeric(NROW(meshP))
BoundConx[1:NROW(meshP)] = BoundCony[1:NROW(meshP)] = 1
BoundConx[c(10, 11, 12)] = BoundCony[c(10, 11, 12)] = 0
SFShear = 0
SFTensile = 0
Length = dime$TrussLength
area = dime$Area
Fx = 10
Fy = 10

fea_stress = FEMStress.2d(meshP, meshT, centroid, BoundConx, BoundCony, SFShear, SFTensile,
             Length, area, Fx, Fy, Y, Nu, Thick)