R/ExpandEM.2d.R

In FEA: Finite Element Modeling for R

#' @title ExpandEM.2d
#'
#' @description Generates the expanded element matrix, which represents the contribution of individual finite elements towards the global structural matrix
#'
#' @usage ExpandEM.2d(meshP, meshT, centroid, EMatrixlist)
#'
#' @param meshP Matrix (2 x n) containing coordinate points of the mesh nodes.
#' @param meshT Matrix (3 x n) containing the number of the coordinate point that forms a given triangle within the mesh.
#' @param centroid Matrix (2 x n) containing coordinate points of the centroid of each triangular element.
#' @param EMatrixlist EMPStress or EMPStrain generated from ElementMat function. List of element matrices.
#'
#' @return Produces large (n x n) matrix.
#' \item{ExpandedMat}{The expanded element matrix}
#'
#' @examples
#' data(triMesh)
#' data(fea_EM)
#'
#' meshP = triMesh$MeshPts$p
#' meshT = triMesh$MeshPts$T
#' centroid = triMesh$Centroids
#' EMatrixlist = fea_EM$EMPStress
#'
#' fea_ExEM = ExpandEM.2d(meshP, meshT, centroid, EMatrixlist)
#'
#' @export


ExpandEM.2d = function(meshP, meshT, centroid, EMatrixlist){
  m= n= z= o= NROW(meshT)
  TDOF = 2*NROW(meshP)

  Expanded_EM = function(meshT, TDOF, centroid, EMatrixlist){
    Expanded = matrix(0, nrow=TDOF, ncol = TDOF)
    r1=2*meshT[m,1]-1
    r2=2*meshT[m,1]
    r3=2*meshT[m,2]-1
    r4=2*meshT[m,2]
    r5=2*meshT[m,3]-1
    r6=2*meshT[m,3]
    Expanded[c(r1,r2,r3,r4,r5,r6),c(r1,r2,r3,r4,r5,r6)] = EMatrixlist[[m]][c(1,2,3,4,5,6), c(1,2,3,4,5,6)]
    return(Expanded)}

  #Run for acquiring individual expanded element matrix=Expanded
  ExpandedMat = list()
  for (m in 1:z){
    ExpandedMat[[m]] = Expanded_EM(meshT, TDOF, centroid, EMatrixlist)}
  return(ExpandedMat)}