3D FEA Studio turns a rectangular beam or cube into an interactive structural study you can rotate, section, and inspect in the browser. It follows the finite element workflow end to end — idealize the geometry, define the material, restrain it, load it, run the analysis, then interrogate the result — and pairs closed-form cantilever theory for the stress field with a genuine incremental plasticity material model, so yielding and plastic history are computed step by step. This page walks through what the studio computes at each stage.
The maths runs in two complementary halves:
The result is an incremental plasticity engine driven by beam theory, wrapped in a full FEA workflow and post-processor. Within slender-beam territory it reproduces textbook cantilever behaviour and post-yield history faithfully — and it does it fast enough to explore interactively.
Choose a rectangular beam or cube and enter its dimensions in metres. Beam models take independent length, width, and height; cube models take one side length used in all three directions.
The shape is built as a subdivided box surface. Its vertices are the points at which every result is later evaluated, so the geometry defines both what you see and where the studio samples the solution.
Pick one of the twelve material presets or type your own values for Young's modulus, Poisson's ratio, density, yield strength, isotropic hardening modulus, ultimate strength, and thermal expansion.
Young's modulus and Poisson's ratio set the elastic response. Yield strength and the hardening modulus drive the incremental plasticity update, and ultimate strength feeds the safety factors shown in the node inspector. Density and thermal expansion are carried with the project through saves and exports, so a full material card travels with the study.
Selecting a fixed face tells the studio which box axis is the beam axis and which end is the built-in end. The span, the cross-section, and the direction the beam deflects all follow from that choice, and a marker highlights the selected face in the viewport.
The face selection parameterises the cantilever formulation, so switching it re-poses the whole study — a long slender bend becomes a short stiff one with a single click.
Add force rows by choosing an axis, a direction, and a magnitude in newtons. All rows are summed into a single resultant, which is applied as a point load on the free face opposite the fixed support.
That resultant is then resolved by the studio: the component along the beam axis becomes a uniform axial stress of force over cross-sectional area, and the dominant cross-axis component becomes the transverse load that produces bending and parabolic shear. The reaction summary reports the full applied resultant and the moment it generates about the support plane.
The mesh slider sets how finely the box surface is subdivided, which controls how many points the field is sampled at. Finer settings give smoother contours, a denser grid to hover over, and a closer look at where the peak values sit.
This is where the numerical work happens. The target strain field is divided into equal load increments — 24 by default, adjustable from 1 to 200 — and every sample point is stepped through them in order:
σy + H·ε̄pBecause the update is path-dependent, increment count matters: more increments trace the loading path more finely once yielding starts. Plastic history also accumulates across successive runs — reload the model repeatedly and plastic strain builds up, exactly as it would in reality. Clear plastic history resets it, as does changing the geometry, mesh density, material, or support face.
Contour the model by von Mises stress, maximum principal stress, maximum shear stress, total strain magnitude, equivalent plastic strain, yielded flag, displacement magnitude, or displacement along X, Y, or Z. Principal stresses come from a closed-form eigenvalue solution of the stress tensor at each point.
Post-processing controls include:
Rotate, pan, zoom, or jump to a camera preset to compare contour patterns and deformation from any angle.
How to read the panels:
Displacements follow the deformation-scale setting throughout the viewport, the inspector, and the exports, and are clamped so the model stays in frame. That makes them a consistent basis for comparing one point, load case, or material against another.
Reactions come from rigid-body statics: the reaction force is the negative of the applied resultant, and the moment is its cross product with the lever arm to the support plane.
Safety factors appear in the node inspector as yield or ultimate strength divided by the von Mises stress at that point, displayed as ≥5.00 once they get large. A value below one marks a point that has passed yield — which the plasticity model has already accounted for.
The plot panel traces the current result array across the displayed mesh, giving a quick profile of how the value varies over the model.
The elastic reference panel compares the result against the analytical cantilever prediction, so once plasticity is active it shows exactly how far the response has departed from the linear answer.
Save the current project in the browser for quick reopening, or export it as JSON for a portable copy. Imported JSON is validated and clamped before it is applied, so a hand-edited file is brought safely into range on load.
Computed values can be exported as a spreadsheet listing each node's displacement, current result value, equivalent plastic strain, and yielded flag. The report option produces a standalone HTML summary of the material, geometry, force count, increment count, and the maximum result, displacement, and plastic strain, together with the number of yielded nodes.
The studio is built to be exact in a well-defined domain rather than approximate across a wide one. Inside that domain the elastic stresses and the post-yield history are computed correctly and behave the way the textbook says they should.
It is at its strongest for:
3D FEA Studio is an educational browser tool for building intuition about bending, yielding, and plastic history. Design work that has to be qualified belongs in a validated finite element package with engineering review.
The workflow this studio models — idealize the geometry, define the material, restrain it, load it, solve, then interrogate the result — is the working pattern of finite element analysis, which is used across engineering disciplines including:
By allowing engineers to evaluate designs before manufacturing, FEA reduces development costs, shortens design cycles, and improves product safety and performance.
3D FEA Studio makes structural behaviour legible in a browser tab. It uses the same workflow a commercial package would — geometry, material, support, load, run, post-process — so the concepts transfer, while keeping the underlying maths small enough to read and reason about: closed-form beam theory for the stresses, and a textbook radial-return algorithm for what happens once those stresses pass yield.
That makes it a tool for building intuition. Change the hardening modulus and watch the yield surface expand; reload a yielded beam and watch plastic strain accumulate; refine the sampling and see where the peak stress sits. Every idea it teaches is the same one you carry into a validated finite element package on real design work.