Structural¶

Statically inteterminate reaction force analysis VM001¶

An assembly of three cylinder bars is supported at both end surfaces. Forces \(F_{1}\) and \(F_{2}\) is applied on the middle of the assembly as shown in Figure [fig:ch5_vm_001_schematic].

finite_element_analysis_welsim_verification_1_schematic

The input data about material, geometry, and loads are given in Table [tab:ch5_vm_001_parameters].

Material Properties	Geometric Properties	Boundary Conditions
Young's Modulus E=2e11	h=10	\(F_{1}\)=2000
Mass Density \(\rho\)=7850	a=3	\(F_{2}\)=1000
Poission's Ratio v=0.3	b=3

The geometries and imposed boundary conditions are shown in Figure [fig:ch5_vm_001_bc].

finite_element_analysis_welsim_verification_1_geometry

The result comparison is given in Table [tab:ch5_vm_001_result].

Results	Theory	WELSIM	Error (%)
Z Reaction Force at Top Fixed Support	1800	1810	0.556
Z Reaction Force at Bottom Fixed Support	1200	1202	0.167

This test case project file is located at [vm/VM_WELSIM_001.wsdb].

Rectangular plate with circular hole subjected to tensile pressure VM002¶

A rectangular plate with a circular hole is fixed along one of the end faces. A tensile pressure load is imposed on another end face as shown in Figure [fig:ch5_vm_002_schematic].

finite_element_analysis_welsim_verification_2_schematic

The input data about material, geometry, and loads are given in Table [tab:ch5_vm_002_parameters].

Material Properties	Geometric Properties	Boundary Conditions
Young's Modulus E=2e11	a=15	Pressure P=1e4
Poission's Ratio v=0.3	b=7.5
	c=2.5
	d=5
	thickness=1

The geometries and imposed boundary conditions are shown in Figure [fig:ch5_vm_002_bc].

finite_element_analysis_welsim_verification_2_geometry

The result comparison is given in Table [tab:ch5_vm_002_result].

Results	Theory	WELSIM	Error (%)
Maximum Normal X Stress	3.125e4	3.156e4	0.992

This test case project file is located at %Installation Directory%/vm/VM_WELSIM_002.wsdb.