Formula Definition Archives - ESRD https://www.esrd.com/product-tag/formula-definition/ Engineering Software Research and Development, Inc. Mon, 23 Jan 2023 21:25:37 +0000 en-US hourly 1 https://wordpress.org/?v=6.6.2 https://www.esrd.com/wp-content/uploads/cropped-SC_mark_LG72ppi-32x32.jpg Formula Definition Archives - ESRD https://www.esrd.com/product-tag/formula-definition/ 32 32 StressCheck Demo: Thermo-Mechanical Analysis with Temperature-Dependent Material Properties https://www.esrd.com/resource-library/product/stresscheck-demo-thermo-mechanical-analysis-with-temperature-dependent-material-properties/ Wed, 18 Jan 2023 19:10:09 +0000 https://www.esrd.com/?post_type=product&p=27037 Abstract: A thermo-mechanical (Heat Transfer -> Elasticity) analysis is performed for a Handbook model of two Inconel 718 connected pipes connected by a thin fin (\Handbook\Tutorial\ConnectedPipes.scw). The parametric Handbook model contains formula-based, temperature-dependent coefficients of thermal conductivity (when the theory is Heat Transfer) as well as formula-based, temperature-dependent linear isotropic material properties (when the theory is Elasticity). The goals of the thermo-mechanical analysis are to:
  • Compute the linear (coefficient of thermal conductivity for a reference temperature T=200 °F) and material nonlinear (coefficient of thermal conductivity is allowed to be temperature-dependent) temperature distributions via steady-state conduction heat transfer
  • Apply the temperature distribution computed from the material nonlinear solution as a thermal load for all elements using a reference temperature of 0 °F
  • Solve a linear elastic solution using the thermal load, symmetry/rigid body constraints, and temperature-dependent linear isotropic properties
  • Extract the local stresses at the intersection of the fin and the pipes.
  For the steady-state conduction heat transfer analysis, the following boundary conditions are assigned:
  • Cooling of the external pipe surfaces is by convection via parameters "Hc" (convective film coefficient) and  "Tc"(convective temperature).
  • The left pipe inside temperature is given by parameter "To", and the right pipe inside temperature is given by parameter "Tp".
  For the linear elastic analysis, the following boundary conditions are assigned:
  • Thermal loading of the connecting pipes + fin is defined by importing the temperatures from the material nonlinear steady state conduction heat transfer solution.
  • Double-symmetry conditions are used to model 1/4 of the connecting pipes + fin.
  • A nodal constraint in the global X direction restricts rigid body translation.
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]]> StressCheck Tutorial: I-Section with Racetrack Cutout Stress Analysis Part 2 – Formula Inputs https://www.esrd.com/resource-library/product/stresscheck-tutorial-i-section-with-racetrack-cutout-stress-analysis-part-2-formula-inputs/ Fri, 11 Feb 2022 22:44:40 +0000 https://www.esrd.com/?post_type=product&p=24083 Abstract: In part 2 of this two-part tutorial series, we will load the boundary layer-meshed model from part 1, define and assign conditional formula expressions for the elastic modulus and applied stress, re-solve, and plot the updated results.]]>
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]]> Helpful Hints and Tips: Stress Transformation Formulae for Results Processing https://www.esrd.com/resource-library/product/helpful-hints-and-tips-stress-transformation-formulae-for-results-processing/ Mon, 26 Aug 2019 17:33:21 +0000 https://esrd.com/?post_type=product&p=11396 Stress transformation formulae, in terms of the normal (Sx, Sy, Sz) & shear (Txy, Tyz, Txz) stresses, may be either input manually in the Formulae window OR imported as a .PAR file for advanced results processing. The following stress transformation formulae are included in the below download as an importable .PAR file and companion SCW:
  • Stress Invariants
  • 1st Principal Stress (2D/3D)
  • 2nd Principal Stress (2D/3D)
  • 3rd Principal Stress (3D)
  • von Mises Stress (2D/3D)
  • Max Shear Stress (2D/3D)
  Note: the error messages may be ignored during .par importation.]]>
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]]> StressCheck Tutorial: Computation of Cross Section Centroid https://www.esrd.com/resource-library/product/stresscheck-tutorial-computation-of-cross-section-centroid/ Thu, 22 Aug 2019 12:04:04 +0000 https://esrd.com/?post_type=product&p=11369 Abstract: Using intrinsic functions SPCTRX, SPCTRY and SPCTRZ to compute the global X, Y, Z locations of a cross section centroid. The locations are computed through the application of a "dummy" traction (with X=SPCTRX/SPAREA, Y=SPCTRY/SPAREA and Z=SPCTRZ/SPAREA) to the surface or surfaces representing the cross section, and then performing a load check to return the X, Y, Z locations of the centroid.]]>
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]]> StressCheck Tutorial: Defining and Assigning a Parabolic Shear Stress Formula Distribution https://www.esrd.com/resource-library/product/stresscheck-tutorial-defining-and-assigning-parabolic-shear-stress-formula-distribution/ Mon, 03 Jun 2019 02:34:14 +0000 https://esrd.com/?post_type=product&p=10619 Abstract: Defining and assigning a parabolic shear stress distribution as a formula expression, and then combining with axial and bending stress formulae to self-equilibrate a bearing loaded lug model.]]>
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]]> Helpful Hints and Tips: Representing the Directional Components of a Bearing Traction Distribution https://www.esrd.com/resource-library/product/helpful-hints-and-tips-representing-directional-components-bearing-traction-distribution/ Tue, 07 May 2019 19:54:25 +0000 https://esrd.com/?post_type=product&p=10285 Abstract: Representing the in-plane directional components of a bearing load traction distribution via customized formulae. Including "heel-to-toe" effects of bending on the in-plane directional tractions.]]>
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]]> StressCheck Tutorial: Solid Modeling of Threaded Holes https://www.esrd.com/resource-library/product/stresscheck-tutorial-solid-modeling-of-threaded-holes/ Fri, 26 Apr 2019 02:31:00 +0000 https://esrd.com/?post_type=product&p=10183 Abstract: Converting helical formula curves into solid threads of any number of turns. Useful in parametric modeling of threaded holes and fasteners.]]>
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]]> Helpful Hints and Tips: Defining a Formula Bearing Load on a Tapered Hole https://www.esrd.com/resource-library/product/helpful-hints-and-tips-defining-formula-bearing-load-on-a-tapered-hole/ Mon, 08 Apr 2019 21:27:16 +0000 https://esrd.com/?post_type=product&p=10036 Abstract: Representing a bearing load distribution via customized formula. Accounts for tapered holes by limiting the height of the bearing load formula.]]>
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]]> Helpful Hints and Tips: Applying a Bending Moment to a Hole Using Formulae https://www.esrd.com/resource-library/product/helpful-hints-and-tips-applying-bending-moment-to-hole-using-formulae/ Mon, 08 Apr 2019 21:21:15 +0000 https://esrd.com/?post_type=product&p=10031 Abstract: Representing the heel-toe effect of a bending moment on a hole bearing distribution via formula traction superposition.]]>
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]]> StressCheck Tutorial: Modeling and SIF Extraction for a 3D Loaded Crack Face https://www.esrd.com/resource-library/product/stresscheck-tutorial-modeling-and-sif-extraction-3d-loaded-crack-face/ Mon, 17 Dec 2018 21:22:01 +0000 https://esrd.com/?post_type=product&p=8666 Abstract: Defining and assigning a formulaic, normal residual stress distribution to a part-thru crack surface, then using the Contour Integral Method - Loaded Crack (CIM-LC) to extract stress intensity factors (SIF) for a 3D plate + hole with loaded corner crack.]]>
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