PROBLEM DESCRIPTION

In this example a rectangular plate, modeled with shell elements, is subjected to an out-of-plane (Z direction) uniform load and an out-of-plane center concentrated load. The uniform and concentrated loads are applied in different load cases. The plate center displacement in the direction of the load is compared with independent hand calculated results for each load case.
The geometry, properties and loading are as suggested in MacNeal and Harder 1985. The plate is 2 inches wide and is modeled with both a 2 inch and a 10 inch length. As suggested in MacNeal and Harder 1985, only a quarter of the plate is modeled. Both a 4x4 and a 16x16 mesh are considered for the quarter plate.
Only the Uz, Rx and Ry degrees of freedom are active in the model. In the 4x4 mesh, model symmetry conditions are imposed by restraining the Rx degree of freedom at joints 22, 23 and 24; restraining the Ry degree of freedom at joints 10, 15, and 20; and restraining both the Rx and Ry degrees of freedom at joint 25. Similar symmetry restraints are used in the 16x16 mesh model. Note that because only a quarter of the plate is modeled, only a quarter of the specified concentrated load is applied to the center of the plate at joint 25.

GEOMETRY, PROPERTIES AND LOADING

App

Object Link: https://openbrim.org/objid23u6l3vlaq7wi5c3stu5zm.project

Library

Object Link: https://openbrim.org/objidfn0rzmvma4uch22al2rno.libobj

Thin Plate Option - Uniform Load - 2x2 Plate

Edge Support	Mesh	Model	Output Parameter	OpenBrIM	Sap2000	Independent	Percent Difference (SAP2000 vs Independent)	Percent Difference (OpenBrIM vs Independent)
Simple	4x4	A	Uz in Center of Plate	4.06	4.06	4.06	0%	0%
Simple	16x16	E		4.06	4.06	4.06	0%	0%
Fixed	4x4	B		1.32	1.32	1.26	5%	4.8%
Fixed	16x16	F		1.27	1.27	1.26	1%	0.8%

Thin Plate Option - Uniform Load - 2x10 Plate

Edge Support	Mesh	Model	Output Parameter	OpenBrIM	Sap2000	Independent	Percent Difference (SAP2000 vs Independent)	Percent Difference (OpenBrIM vs Independent)
Simple	4x4	C	Uz in Center of Plate	12.86	12.86	12.97	-1%	-0.84%
Simple	16x16	G		12.96	12.96	12.97	0%	0%
Fixed	4x4	D		2.60	2.60	2.60	0%	0%
Fixed	16x16	H		2.60	2.60	2.60	0%	0%

Thin Plate Option - Center Concentrated Load - 2x2 Plate

Edge Support	Mesh	Model	Output Parameter	OpenBrIM	Sap2000	Independent	Percent Difference (SAP2000 vs Independent)	Percent Difference (OpenBrIM vs Independent)
Simple	4x4	A	Uz in Center of Plate	11.94	11.94	11.60	3%	3%
Simple	16x16	E		11.63	11.63	11.60	0%	0.26%
Fixed	4x4	B		5.90	5.90	5.60	5%	5%
Fixed	16x16	F		5.64	5.64	5.60	1%	0.7%

Thin Plate Option - Center Concentrated Load- 2x10 Plate

Edge Support	Mesh	Model	Output Parameter	OpenBrIM	Sap2000	Independent	Percent Difference (SAP2000 vs Independent)	Percent Difference (OpenBrIM vs Independent)
Simple	4x4	C	Uz in Center of Plate	18.12	18.12	16.95	7%	7%
Simple	16x16	G		17.15	17.15	16.95	1%	1%
Fixed	4x4	D		7.79	7.79	7.25	7%	7%
Fixed	16x16	H		7.41	7.41	7.25	2%	2%

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