Structural Mechanics & FEM
Research-Grade FEA Beam Simulator
Examine elastic bending moment profiles, nodal shear step responses, and transient structural vibrations of pre-loaded beams utilizing a 1D Euler-Bernoulli/Timoshenko finite stiffness solver.
Max Displacement
3.023 mm
Dynamic tip deflection
Fundamental Freq.
40.8 Hz
Elastic natural mode
Safety factor (FOS)
3.78
Yield threshold limit
Parameters
Material Selection
Boundary Conditions
Cross-Section profile
Step response vibration transient
Deep Beam Finite Element Discretization Governing Equations
1D Timoshenko Stiffness
[K_T^e] = beta * EI/Le^3 * Matrix(12, 6Le, -12, 6Le...)
Shear Parameter (Deep Beams)
Phi = 12*E*I / ( G * As * Le^2 )
Viscous Dynamic Oscillation
u(t) = u_static * (1 - exp(-zeta*wn*t) * (cos(wd*t) + ...))
Extreme Bending Stress
sigma_bending = (M * y_max) / I_y
deep beam structures are solved incorporating Timoshenko shear factors to avoid standard mesh shear locking.
Discretized stiffness equations are resolved at each node using real-time direct Gauss elimination.
Bending moment (BMD) and shear force (SFD) diagrams are plotted dynamically under the beam coordinate plane.
Nodal Finite Element Deflection Profile
Static Deflection (Tip)
3.0234mm
Moment of Inertia (I_y)
0.000067m⁴
Max Bending Stress
66.06MPa
Static Factor of Safety
3.78
Bending stress vs Beam Position (Discretized Nodes)
Nodal Displacement Profile Table
| Coordinate x (m) | Deflection (mm) | Bending Stress (MPa) | Bending Moment (N·m) |
|---|---|---|---|
| 0.00 m | 0.0000 mm | 66.06 MPa | -44040 N·m |
| 0.13 m | -0.0211 mm | 63.06 MPa | -42040 N·m |
| 0.27 m | -0.0796 mm | 60.06 MPa | -40040 N·m |
| 0.40 m | -0.1727 mm | 57.06 MPa | -38040 N·m |
| 0.53 m | -0.2978 mm | 54.06 MPa | -36040 N·m |
| 0.67 m | -0.4522 mm | 51.06 MPa | -34040 N·m |
| 0.80 m | -0.6334 mm | 48.06 MPa | -32040 N·m |
| 0.93 m | -0.8385 mm | 45.06 MPa | -30040 N·m |
| 1.07 m | -1.0649 mm | 42.06 MPa | -28040 N·m |
| 1.20 m | -1.3100 mm | 39.06 MPa | -26040 N·m |
| 1.33 m | -1.5712 mm | 36.06 MPa | -24040 N·m |
| 1.47 m | -1.8456 mm | 33.06 MPa | -22040 N·m |
| 1.60 m | -2.1307 mm | 30.06 MPa | -20040 N·m |
| 1.73 m | -2.4238 mm | 27.06 MPa | -18040 N·m |
| 1.87 m | -2.7223 mm | 24.06 MPa | -16040 N·m |
| 2.00 m | -3.0234 mm | 22.56 MPa | -15040 N·m |