Analysis of Membrane Wrinkling (Rimpling)
Analysis of Membrane Wrinkling (Rimpling): Theoretical Foundations
What is Membrane Wrinkling?
Professor, what kind of phenomenon is wrinkling (rimpling) in membrane structures?
Membrane structures have almost zero bending stiffness. When compressive stress occurs, wrinkles form. This becomes a problem in space solar panels, airbags, and tent structures.
Mechanics of Wrinkling
When compressive stress occurs in a membrane:
1. The membrane cannot withstand compression — buckling = wrinkling due to lack of bending stiffness
2. Wrinkle direction — wrinkles form orthogonal to the compression direction
3. Wrinkle wavelength — depends on membrane tension, plate thickness, and curvature
Modeling in FEM
Two approaches:
1. Shell elements (thin thickness) — Directly simulate wrinkle shape. NLGEOM=YES + initial imperfection for buckling → wrinkle
2. Membrane elements (zero bending stiffness) + wrinkle model — "Tension field theory" that sets compressive stress to zero
Can't membrane elements directly represent wrinkles?
Membrane elements have no bending stiffness, so the "shape" of wrinkles does not appear under compression. Instead, compressive stress is set to zero to obtain the "stress field in the wrinkled state." Abaqus's *NO COMPRESSION or membrane wrinkle algorithms.
Summary
Origin of Tank Liquid Sloshing and Membrane Wrinkling Theory
Membrane wrinkling theory originated from the difference between tension and compression. The distinction between "tension membranes" where wrinkles do not occur and "wrinkled membranes" with compressive stress was made by Stein & Hedgepeth (1961, NASA). They established the "relaxed principal stress theory" where stress in the principal compression direction is set to 0 in wrinkled regions. The theoretical foundation of current FEM wrinkle analysis lies in this 1961 paper.
Computational Methods for Analysis of Membrane Wrinkling (Rimpling)
Shell Element Approach (Obtaining Wrinkle Shape)
```
*SHELL SECTION
0.025, 5 $ Plate thickness 0.025mm (membrane)
*STEP, NLGEOM=YES
*STATIC, RIKS $ Wrinkling is a type of buckling
```
Give an initial imperfection (first buckling mode shape) to manifest the wrinkle pattern.
Membrane Element Approach (Tension Field)
```
*MEMBRANE SECTION
0.025
*NO COMPRESSION $ Set compressive stress to zero
```
Wrinkle shape does not appear, but the stress field in wrinkled regions is obtained.
Summary
Wrinkle Finite Element Method: Modified Material Property Method
Methods for handling membrane wrinkles in FEM include: ① "Relaxed stiffness method" that clips principal stress to zero, ② "Analytical tracking method" that calculates only non-wrinkled regions, ③ "Buckling analysis method" that reproduces actual geometric wrinkles with fine meshes. In practice, the modified material property method (relaxed stiffness method) is the most robust, and the combination of Abaqus membrane element M3D4R and Wrinkle determination subroutine is widely used in industry.
Analysis of Membrane Wrinkling (Rimpling) in Practice
Practical Wrinkle Analysis
Most important in space structures (solar panels, membrane structure antennas). Wrinkles degrade optical surface accuracy.
Practical Checklist
Deployed Membrane Analysis for Space Solar Power Satellites
Thin-film solar panels (thickness 0.01mm) for Space Solar Power Satellites (SSPS) may experience thermal deformation and wrinkles after deployment. Since the 2010s, JAXA has conducted thermal-structural coupled wrinkle analysis of polyimide films (thickness 12.5μm), identifying that wrinkles with 3-5mm wavelength caused by the combination of solar radiation pressure and thermal expansion affect power generation efficiency, and reflected this in membrane tension design.
Analysis of Membrane Wrinkling (Rimpling): Software & Solver Comparison
Wrinkle Analysis Tools
Special Settings for Thin Film Analysis in Ansys Mechanical
Ansys Mechanical's Shell181 or Membrane elements (SHELL181, KEYOPT(1)=1) function as pure membrane elements with zero out-of-plane stiffness. Wrinkle determination is typically implemented by combining material input that only permits "principal stress ≥ 0" (USERFLD + relaxed stiffness subroutine). ESA used this method for designing Europe's large membrane antenna (diameter 15m) for spacecraft, predicting on-orbit wrinkle shape with ±3% accuracy.
Advanced Technology
Advanced Wrinkle Research
Singular Field at Wrinkle Tip and Effective Membrane Thickness
In membranes where wrinkles spread, the actual effective thickness becomes "membrane thickness ÷ number of wrinkles", significantly reducing equivalent bending stiffness. Molecular dynamics simulation of a 0.1mm thick aluminum foil wrinkle tip in the 2020s revealed that local stress reaches 3-5 times the bulk yield stress. This high local stress is a key parameter determining crack initiation life in folded space deployable structure lifespan design.
Analysis of Membrane Wrinkling (Rimpling): Common Issues & Debugging
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