Calculator Inputs
Example Data Table
| Parameter | Example Value | Meaning |
|---|---|---|
| L | 2 m | Element length |
| A | 0.005 m² | Cross section area |
| E | 200000000000 Pa | Elastic modulus |
| u1, u2 | 0 m, 0.001 m | Nodal displacements |
| q | 1000 N/m | Uniform axial load |
| P | 500 N at a/L 0.5 | Interior point load |
| Delta T | 20 | Temperature change |
Formula Used
The calculator uses a two node axial finite element. For a bar element, stiffness is calculated as:
k = EA / L
The local stiffness matrix is:
[k] = k [[1, -1], [-1, 1]]
The mechanical nodal force vector is:
{f mechanical} = [k]{u}
The thermal correction is:
{f thermal} = EA alpha DeltaT [1, -1]
The equivalent distributed load is:
{f q} = qL / 2 [1, 1]
The equivalent point load is:
{f P} = P [1 - a/L, a/L]
The residual nodal force is:
{R} = {f internal} - {f external}
How to Use This Calculator
Enter values using one consistent unit system. Use meters, square meters, pascals, and newtons for SI work. You can also use another consistent system. Change the force unit label to match your project.
Choose the bar model when area, modulus, and length define stiffness. Choose the spring model when you already know stiffness. Add nodal displacement values with correct signs. Then add distributed load, point load, body load, thermal expansion, and load factor if needed.
Press Calculate to view internal nodal forces, equivalent loads, residuals, balancing forces, strain, stress, and axial force. Use CSV for spreadsheet records. Use PDF for a compact report.
Advanced Guide to FEA Nodal Force Calculation
What This Calculator Does
Finite element analysis divides a body into small elements. Each element connects through nodes. Forces at those nodes describe how the element pushes or pulls on the global model. This calculator focuses on a two node axial element. It is useful for bars, ties, rods, springs, and simplified structural members.
Why Nodal Forces Matter
Nodal forces help verify equilibrium. They also help locate support reactions. When displacement results are known, the stiffness matrix can recover internal force. Applied loads are then converted into equivalent nodal loads. The difference gives a residual force. A small residual usually means the element is balanced.
Input Planning
Use one unit system from start to finish. Mixing inches with meters or pounds with newtons will create wrong answers. The length controls stiffness strongly. The area and elastic modulus also affect bar stiffness. A higher modulus or larger area raises force for the same displacement.
Load Options
The calculator includes several load sources. A uniform distributed axial load is split equally between nodes. A point load is shared by linear shape functions. Body force uses density, area, and acceleration. Thermal strain is handled as an initial strain effect. It can create force even when displacement is zero.
Reading the Result
Internal nodal force comes from stiffness, displacement, and thermal strain. Equivalent external load comes from applied actions. Residual force shows the unbalanced amount at each node. Balancing force is the opposite value. Engineers often use it as a reaction or correction estimate.
Engineering Use
This tool is best for checking hand calculations, teaching element behavior, or preparing quick comparison data. It does not replace a full solver for complex geometry. Use it with engineering judgment. Check sign convention, boundary conditions, and model assumptions before using results in design.
FAQs
What is a nodal force in FEA?
A nodal force is the force represented at an element node. It may come from stiffness, displacement, applied loads, body force, or thermal strain.
Can this calculator handle thermal strain?
Yes. Enter thermal expansion coefficient and temperature change. The calculator adds the thermal nodal force correction for an axial bar element.
What unit system should I use?
Use one consistent unit system. For SI, use meters, square meters, pascals, newtons, kilograms per cubic meter, and meters per second squared.
What does residual nodal force mean?
Residual nodal force is internal force minus equivalent external load. It shows the remaining unbalanced force at each node.
What is the balancing force?
The balancing force is the negative of the residual force. It can represent the force needed to satisfy equilibrium at a node.
When should I use custom stiffness?
Use custom stiffness for a spring element or when stiffness is known from testing, manufacturer data, or another calculation.
Does this solve a full FEA model?
No. It calculates one element response. A full model needs assembly, boundary conditions, global solving, and post processing.
Why are signs important?
Signs define force and displacement direction. A wrong sign can reverse tension, compression, support reactions, and residual force values.