Structural simulation

About studies

A study is a simulation of a part or an assembly. Meridian uses the finite element method (FEA). The solid mesh uses 10-node tetrahedral elements. Thin parts can use shell elements.

A study has:

The bodies to analyze and their material.
The mesh settings.
The supports and the loads on faces.
The thermal conditions, if the study has heat.

Meridian saves the studies in the .mpart or .massy file. Meridian does not save the results. Run the study again to get the results.

Study kinds

All study commands are on the Simulation tab, in the Study group.

Command	What it calculates
New Static Study	The stress and the displacement of the part.
New Modal Study	The natural frequencies of the part.
New Thermal Study	The temperature and the heat flow in the part.
New Buckling Study	The load at which the part buckles.
New Harmonic Study	The response of the part to loads that change as a sine.
New Transient Study	The response of the part to loads that change with time.
New Flow Study (Beta)	The fluid flow around or through the part. Refer to Fluid simulation.

Other commands in the Study group:

Study Settings changes the material and the settings of the active study.
Fatigue Settings sets the load cycle and the S-N data for the fatigue life of a static study.
Nonlinear Settings sets the load steps, the large displacement and the plasticity of a nonlinear static study.
Copy Study makes a new study with the same settings, supports and loads.

Run a static study

Open the part.
On the Simulation tab, click New Static Study.
Click Study Settings and make sure that the material is correct.
Click Fixed Support and select the faces that cannot move.
Click Force and select the faces that get the load. Enter the force.
Click Mesh Settings and set the element size. Start with a coarse mesh.
Click Run.
Click Von Mises to see the stress. Click Factor of Safety to see the safety margin.

The start page has a guided tour for a stress study, and a template "plate with a study".

Supports

Support	What it does
Fixed Support	Holds faces so that they cannot move.
Roller	Lets faces slide in their plane, but not move through it.
Pinned	Lets cylindrical faces turn about their axis only.

Loads and connectors

Load	What it does
Force	Applies a total force to faces.
Pressure	Applies a pressure to faces.
Gravity	Applies an acceleration to the whole part.
Remote Force	Applies a force that acts at a point away from the faces.
Moment	Applies a moment to faces about a point, with no force.
Temperature Change	Applies a uniform temperature change to the part.
Temperature From Study	Applies the temperatures of a thermal study to the part.
Bearing Load	Applies a radial force to a hole or a shaft as a cosine pressure.
Bolt	Connects two coaxial holes with a bolt that has a preload.
Spring	Connects faces to other faces, or to the ground, with a spring.
Remote Mass	Attaches a point mass with rotary inertia to faces.

Bolts

A bolt goes between two coaxial holes. It has a diameter, a property class and a preload. You can give the preload as a force or as a torque. For a torque, Meridian uses F = T / (K d), with K = 0.2 as the default. Meridian applies the preload in a first step.

A nonlinear study does not accept connectors. A modal, buckling or dynamic study does not use the preload.

Thermal conditions

Condition	What it does
Fixed Temperature	Holds faces at a temperature.
Heat Flux	Applies a heat flux to faces.
Heat Power	Applies a total heat power to faces.
Convection	Lets faces exchange heat with a fluid.
Heat Generation	Makes heat in the full volume of the part.
Heat From Flow	Lets faces exchange heat with the fluid of a flow study.

A thermal study is steady by default. A transient thermal study has an end time and a time step. The method is backward Euler (the default) or Crank-Nicolson. The default initial temperature is 20 °C. The material must have a specific heat.

Harmonic and transient studies

Harmonic and transient studies use modal superposition. The default is 10 modes. The default damping ratio is 0.02.

A harmonic study has a frequency range. Each load can have a phase.
A transient study has an end time and a time step. Each load can have a load curve: step, ramp, half sine, or a table of time and factor values.

Fatigue

A static study can calculate the fatigue life (stress-life method).

The static loads give the maximum load of the cycle.
Mean-stress correction: none, Goodman, Gerber or Soderberg.
Marin factors for the surface, the size and the reliability, and a notch factor.
The S-N curve can be a Basquin curve or a table. If the material has no curve, Meridian makes an estimate from the ultimate strength. The result tells you that it is an estimate.

Nonlinear static studies

A nonlinear static study can include large displacement and plasticity. The default is 10 load steps. Plasticity uses the von Mises yield criterion with isotropic hardening. You can set a tangent modulus. Use Plastic Strain to see the result.

Contacts in assemblies and multi-body parts

Faces of two bodies that touch get an automatic bonded contact. The gap tolerance is 0.01 mm.
You can set a manual contact pair: bonded, frictionless or no separation.
Only a static study solves frictionless and no-separation contacts. Other study kinds use them as bonded and give a warning.
An assembly study can use the mates as connections. A concentric mate can become a pin, so that the bodies can turn about the axis.

Shell elements

A thin part can use shell elements instead of solid elements. Shell elements need much fewer nodes. For example, a 200 x 200 x 5 mm plate needs about 1,060 shell nodes, but about 552,000 solid nodes.

The part must be one body of one of these shapes:

A flat plate with two parallel faces. The thickness must be at most 0.25 of the width. Holes are permitted.
A thin-walled prism: an extruded section of flat and cylindrical walls. Examples are bent brackets, angles, channels, box sections and tubes.

Shell elements are not available for transient thermal studies, nonlinear studies, fatigue, flow, contacts and connectors. If the part has thin walls that shell analysis does not support, Meridian uses solid elements and gives a warning that starts with "Shell elements are not used".

Use solid elements when the wall thickness is more than about 0.1 of the span.

Mesh

Click Mesh Settings to set the element size and the element order.

Start with a coarse mesh. Make sure that the setup is correct.
Then make the mesh finer and run again. If the result changes much, the mesh is too coarse.
The peak stress is often at sharp inside corners. Look at these areas carefully.
A support on a line (an edge) is singular. Its results do not converge to a fixed value when you make the mesh finer.

Results

Result	What it shows
Von Mises	The von Mises stress.
Displacement	The displacement.
Principal Stress	The largest principal stress.
Factor of Safety	The factor of safety.
Fatigue Life, Fatigue Damage, Fatigue Factor of Safety	The fatigue results of a static study with fatigue settings.
Plastic Strain	The equivalent plastic strain of a nonlinear static study.
Contact Pressure	The pressure of frictionless, no-separation and frictional contacts.
Friction Stress	The friction shear stress of frictional contacts.
Contact Status	The status of frictional contacts: open (0), slip (1) or stick (2).
Mode Shapes	The mode shapes of a modal study.
Unaveraged Stress	The stress of each element, without the average at the nodes.

Read the results

Factor of safety = yield strength / maximum von Mises stress. A value from 1.5 to 3 is usual.
A buckling factor less than 1 means that the part buckles under the load. Buckling factors are linear values. Imperfections can lower the real collapse load.

Result tools

Tool	What it does
Deformed Shape	Shows the result on the deformed shape.
Animate	Moves the part through the deformed shape again and again.
Probe	Shows the result value at the pointer.
Probe Line	Shows the result values on the line between the last two probe points.
Copy Probe Values	Copies the values of the probe points and the probe line as a table.
Clear Probes	Removes all probe points and the probe line.

Reports and export

Report saves a report of the active study as an HTML or Markdown file.
Export Results saves the node results as a CSV file, or as a VTK file for ParaView. This is available for structural and thermal studies.

You can also run studies from the command line with meridian simulate. Refer to Command line.

Accuracy

Meridian checks its solvers against NAFEMS benchmarks and analytic solutions. Refer to Validation.