# Name: 		_README.txt fr Ordner "\03_Multiscale\04"

# Content:		This folder contains all data for the "reinforced Plate"-example using.
				
				The quarter of a rectangular thin plate with longitudinal circular reinforcement is to be investigated. 
				The plate is subjected to a uniformly distributed load p and has dimensions L=B=50 and thickness h=1. 
				Linear-elastic material behaviour is assumed with the following parameters:
					Matrix: E =  27000	nu = 0.2
					Fibre:	E = 142000	nu = 0.35
				
				The boundary conditions and dimensions are given in Fig. 7.23.
				A reference full-scale solution is obtained using standard hexahedral elements with quadratic shape
				functions. All boundary conditions are applied and evaluated at the mid-surface of the RVE. 
				
				The RVE is discretised using a polynomial degree of pb=pc=3 and 8 elements in boundary (nb) and scaling (nc)
				direction, respectively. 
				
				Three different aspects are examined:
					1) In a first step, the macroscopic discretisation is varied, such that a number of numel macroscopic
						shell elements is used (numel = 2x2, 4x4, 8x8, ... 1024x1024). Furthermore, all three types of 
						mesoscopic boundary conditions (tbc, sbc, pbc) and different in-plane RVE sizes (LRVE = 1,2,4) 
						are investigated. The RVE height is constant as h = 1.
					
					2) Next, the complexity of the full-scale approach and the coupled multiscale approach are compared. 
						Again, the number of macroscopic shell elements, the RVE size and the type of mesoscopic boundary
						conditions are varied. The complexity is obtained as
							multiscale: (#macroscopic equations)^2 + #Gausspoints * (#mesoscopic equations)^2
							Full-scale:	(#equations)^2
							
					3) Lastly, for the case of periodic boundary conditions the influence of the mesoscopic discretisation
						is investigated further. To do so, the number of elements is varied nc=nb=2,4,6 and 8.
														
				Abbreviation of the boundary conditions:
				pbc - periodic boundary conditions
				sbc - shell boundary conditions
				tbc - traction boundary conditions
				
				Detailed description may be found in [1].

# Datum:		29.08.2024

# Author:		Leonie Mester

# Files:		Fig_7-23.pdf	- Figure 7.23 from [1], illustration of the quarter of the plate including dimensions 
								  and boundary conditions, (b) shows the full-scale reference configuration
				Fig_7-24.pdf 	- Figure 7.24 from [1], comparison of the displacement uz at point A vs. the number of
								  macroscopic shell elements (numel) for different boundary conditions and RVE sizes
				Fig_7-25.pdf 	- Figure 7.25 from [1], comparison of the displacement uz at point A vs. the complexity
								  of the problem for different boundary conditions and RVE sizes
				Fig_7-26.pdf 	- Figure 7.26 from [1], comparison of the error of the displacement (compared to reference)
								  vs. the complexity of the problem for different RVE discretisations using pbc
								  
				FE2_pbc_RVE1x1x1.dat		- Data for proposed homogenisation approach with periodic boundary conditions (pbc)
											  and RVE size 1x1x1 (discretisation pb=pc=3, nb=nc=8)
				FE2_pbc_RVE1x1x1_Disc.dat	- Data for proposed homogenisation approach with periodic boundary conditions (pbc)
											  and different RVE discretisation (RVE size 1x1x1)
				FE2_pbc_RVE2x2x1.dat		- Data for proposed homogenisation approach with periodic boundary conditions (pbc)
											  and RVE size 2x2x1 (discretisation pb=pc=3, nb=nc=8)
				FE2_pbc_RVE4x4x1.dat		- Data for proposed homogenisation approach with periodic boundary conditions (pbc)
											  and RVE size 4x4x1 (discretisation pb=pc=3, nb=nc=8)
				FE2_sbc_RVE1x1x1.dat		- Data for proposed homogenisation approach with shell boundary conditions (sbc)
											  and RVE size 1x1x1 (discretisation pb=pc=3, nb=nc=8)
				FE2_sbc_RVE2x2x1.dat		- Data for proposed homogenisation approach with shell boundary conditions (sbc)
											  and RVE size 2x2x1 (discretisation pb=pc=3, nb=nc=8)
				FE2_sbc_RVE4x4x1.dat		- Data for proposed homogenisation approach with shell boundary conditions (sbc)
											  and RVE size 4x4x1 (discretisation pb=pc=3, nb=nc=8)
				FE2_tbc_RVE1x1x1.dat		- Data for proposed homogenisation approach with traction boundary conditions (tbc)
											  and RVE size 1x1x1 (discretisation pb=pc=3, nb=nc=8)
				FE2_tbc_RVE2x2x1.dat		- Data for proposed homogenisation approach with traction boundary conditions (tbc)
											  and RVE size 2x2x1 (discretisation pb=pc=3, nb=nc=8)
				FE2_tbc_RVE4x4x1.dat		- Data for proposed homogenisation approach with traction boundary conditions (tbc)
											  and RVE size 4x4x1 (discretisation pb=pc=3, nb=nc=8)
				ref.dat						- Data of reference solution obtained using quadratic hexahedral elements 
				
				
# References:	[1]  	Leonie Mester, Computational Homogenisation and Multiscale Modelling Employing an Image-based
						Approach for the Structural Analysis of Shells, RWTH Aachen, PhD Thesis (2024)
