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Industrial Crane, Noninear Static Analysis

MDA performed nonlinear static stress analysis on this industrial crane boom. This analysis possesses contact nonlinearity where the booms slide into each other on pads as indicated by the arrows in the figure below. One of the load cases for the analysis had the base of the crane mounted on a 20 [ deg ] angle with respect to horizontal with the boom extended parallel to horizontal. This results in high loads on the pinion gear and ring gear on the geared bearing. Our client needed to know the gear tooth loads so they could properly select a pinion gear and geared bearing. We included the geared bearing and pinion gear in the model and used nonlinear gap elements between the pinion gear tooth and geared bearing tooth. Loads were pulled from these elements and used to specify a geared bearing and pinion. Additionally, loads were retrieved from the beam element representing the hydraulic cylinder used to raise and lower the boom. These loads were confirmed against hand calculations by MDA to demonstrate the reasonableness of the FEA results.

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Pinion Adapter, Nonlinear Static Analysis

MDA performed nonlinear static stress analysis on this pinion adapter connection for a robotic positioner. The analysis possesses contact nonlinearity with friction at all the mating surfaces of the assembly. The figure on the bottom left shows the pinion, adapter, and bolt. The adapter had been redesigned by our client and because of space constraints the outside diameter of the adapter is limited and there is only approximately 0.120 [ in ] of material between the major diameter of the internal threads and the outer diameter of the adapter. For this reason, our client requested a FEA be performed to determine the stresses near the threaded connection at the outer diameter of the adapter as shown by the probe in the video. The nonlinear static model took advantage of symmetry by using only a 30 [ deg ] section of the pinion and adapter encompassing one bolt. Threads were not modeled because we only care about load transfer to the adapter from the pinion and bolt. Surface-surface contact was defined between the mating surfaces of the pinion and adapter. Surface-surface contact is also defined between the under-head portion of the bolt and the pinion mating surface. Since bolt stresses are of no concern in the analysis, but load transfer to the assembly is necessary via bolt preload, the nodes on the bottom surface of the bolt shank are constrained to allow translation in the y-direction only and a bolt preload is applied. For force transfer to the adapter, the cylindrical portion of the bolt shank is assigned surface-surface contact with the 20 [ mm ] hole in the adapter. Finally, a tooth load is applied at the pitch radius of the pinion.

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Cylinder Frame, Nonlinear Static Analysis

MDA structurally substantiated a steel frame used to secure 25 high pressure cylinders for transportation. The nonlinear static analysis was performed to D.O.T. SP13173 Paragraph 7.C.8. This analysis was nonlinear because of the use of Gap elements to allow sliding (in one direction only) of the cylinder noses mounted in delrin bushings. Our client provided solid models of the structure and cylinders. A surface model of the structurally substantial members and cylinders was created and imported to finite element software for continued modeling and analysis. Read the report on this project here. This report is representative of a typical analysis report we provide our clients.

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About Nonlinear Static Analysis

A nonlinear analysis is an analysis where a nonlinear relation holds between applied forces and displacements. Nonlinear effects can originate from geometric nonlinearity’s (such as large displacements), material nonlinearity’s (such as elastoplastic material), contact, and nonlinear loading and constraints.

Geometric Nonlinearity

In analyses involving geometric nonlinearity, changes in geometry as the structure deforms are considered in formulating the constitutive and equilibrium equations. Many applications such as metal forming, tire analysis, and medical device analysis require the use of large deformation analytical methods based on geometric nonlinearity. Small deformation analysis based on geometric nonlinearity is required for some applications, like analysis involving cables, arches and shells. Geometric nonlinearity may be characterized as possessing small strains but large rotations.

Material Nonlinearity

Material nonlinearity involves the nonlinear behavior of a material based on a current deformation, deformation history, rate of deformation (strain rate), temperature, pressure, and so on. Examples of nonlinear material models are large strain, plasticity, elastoplasticity, and hyperelasticity (rubber and plastic materials).

Constraint and Contact Nonlinearity

Constraint nonlinearity in a system can occur if kinematic constraints are present in the model. The kinematic degrees of freedom of a model can be constrained by imposing restrictions on its movement.

MDA and Nonlinear Static Analyses

MDA has performed dozens of nonlinear static analyses and we have vast experience in all three types of nonlinearity: geometric, material, contact and constraint. A brief list is shown below:

  • Machine frames
  • Robotic components
  • Heavy machinery
  • Consumer components
  • Component parts
  • Complex assemblies

Experience and skill is required to successfully execute a nonlinear analysis and interpret the results. Care should be taken to specify appropriate model and solution parameters. Understanding the physics of the problem, the role played by the solution parameters, and a planned and logical approach will do much to ensure a successful solution. We have the experience and expertise to successfully execute your nonlinear solution. Click here to view an example of an analysis report we provide.

Our FEA Capabilities
  • Linear
  • Static stress & deflection
  • Dynamic stress & deflection
  • Critical buckling load
  • Nonlinear
  • Thermal
  • Topology optimization
  • Size optimization
  • Geometric
  • Material
  • Contact
  • Postbuckling (Riks)
  • Mechanical event simulation
  • Dynamic stress & deflection
  • Dynamic
  • Modal analysis
  • Frequency response
  • Time response
  • Response spectrum
  • Random vibration
  • Transient stress
  • Explicit & implicit
  • Drop and direct impact events
  • Rotor dynamics
  • Shock and seismic
  • Power train vibration analysis
  • Fatigue life & durability