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David Bushnell, retired Charles Rankin, Rhombus Consultants Group, Inc.

Use of GENOPT and BIGBOSOR4 to obtain optimum designs of axially compressed cylindrical shells with a composite truss-core sandwich wall. David Bushnell, retired Charles Rankin, Rhombus Consultants Group, Inc. 52nd AIAA Structures Meeting, April, 2011 AIAA Paper 2011-xxxx. Summary.

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David Bushnell, retired Charles Rankin, Rhombus Consultants Group, Inc.

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  1. Use of GENOPT and BIGBOSOR4 to obtain optimum designs of axially compressed cylindrical shells with a composite truss-core sandwich wall David Bushnell, retired Charles Rankin, Rhombus Consultants Group, Inc. 52nd AIAA Structures Meeting, April, 2011 AIAA Paper 2011-xxxx

  2. Summary • What is GENOPT? (Slides 3 - 16) • What is BIGBOSOR4? (Slide 17) • General and local buckling models (Slides 18-23) • Huge torus/prismatic shell model (Slide 24) • Various local buckling models (Slides 25-28) • Pre-buckled state of the shell (Slide 29) • Modeling details (Slides 30-33) • “Noodle support” index, ILINKS=0,2,1 (Slides 34-36) • General buckling does not depend on ILINKS (Slide 37) • Optimization (Slides 38-41) • Design sensitivity (Slide 42) • STAGS models for general and local buckling (Slides 43-47) • Conclusions (Slide 48) • STAGS results perhaps to be included in Andrew Lovejoy’s paper (Slides 49-97)

  3. What is BIGBOSOR4? • Stress, buckling and vibration of elastic shells of revolution (BIGBOSOR4=BOSOR4 with more shell segments permitted, up to 295 shell segments as of 2011). • Nonlinear axisymmetric stress analysis • Linear non-axisymmetric stress analysis • Axisymmetric or non-axisymmetric bifurcation buckling • Linear vibration modes of axisymmetrically loaded shell • Multi-segment, branched, ring-stiffened shells of revolution • Various wall constructions • BIGBOSOR4 cannot handle local shell segment transverse shear deformation (t.s.d.) or local shell wall anisotropy or bifurcation buckling with applied in-plane shear loading. Use a factor of safety to compensate for these effects on local buckling.

  4. Part of the cross section of the truss-core sandwich wall of the cylindrical shell used for the general buckling analysis Noodles are modeled as beams and are shown as little green squares located at the centroids of the noodle gaps. There are no little “noodle gap” shell segments. A little more than 5 modules are displayed here.

  5. A typical general buckling mode General buckling models have 46 modules. About 5 modules are shown in the previous slide.

  6. Cross section of the truss-core sandwich wall of the cylindrical shell used for the local buckling analysis. A one-module model for local buckling (ILINKS=0). The 22-segment local buckling model has two noodle beams in each noodle gap. The centroids of these are shown as little green squares.

  7. Cross section of the truss-core sandwich wall of the cylindrical shell used for the local buckling analysis. A one-module model of local buckling (ILINKS=0). Local buckling mode from a one-module model

  8. Cross section of the truss-core sandwich wall of the cylindrical shell used for the local buckling analysis (3-module model) Three-module local buckling model

  9. Cross section of the truss-core sandwich wall of the cylindrical shell used for the local buckling analysis. A three-module model of local buckling (ILINKS=0). Local buckling mode from a three-module model

  10. The “huge torus” model of a prismatic shell. Drawing Robert P. Thornburgh

  11. A one-module model used for local buckling. “noodle support” index, ILINKS=0

  12. A one-module model used for local buckling. “noodle support” index, ILINKS=2 Note that the noodle gap cross section does not change shape in the local buckling mode. Compare with the previous slide.

  13. A one-module model used for local buckling. “noodle support” index, ILINKS=1

  14. A three-module model used for local buckling. “noodle support” index, ILINKS=1 A three-module local buckling model with the “noodle support” index, ILINKS = 1. Noodles are modeled as beams, the centroids of which are indicated by little green squares.

  15. A three-module STAGS model used for local buckling. “noodle support” index, ILINKS=0. STAGS is NOT used for optimization. Purpose of this slide is to display the pre-buckled membrane state assumed in the GENOPT/BIGBOSOR4 models Pre-buckling axial compression, Nx

  16. Cross section of the truss-core sandwich wall of the cylindrical shell used for the local buckling analysis. One elaborate 22-segment module.

  17. Cross section of the truss-core sandwich wall of the cylindrical shell used for the general buckling analysis. One simple 6-segment module.

  18. Computation of discrete ring areas

  19. The composite layup scheme shown here is used in the specific case called “test” [3]. The layup scheme for the specific case called “nasatruss2”, described in this paper, is different from that shown here. Both “test” and “nasatruss2” are members of the generic class called “trusscomp”. Composite laminates

  20. Local buckling of starting design (ILINKS=0) Noodles do NOT support the little shell segments that enclose them

  21. Local buckling of starting design (ILINKS=2) Noodles do support the little shell segments that enclose them. These little “noodle gap” shell segments have high bending stiffness in the plane of the truss-core sandwich cross section in order to simulate this noodle support. The noodle gap cross sections hardly deform at all in this local buckling mode shape.

  22. Local buckling of starting design (ILINKS=1) Noodles do support the little shell segments that enclose them. This noodle support is simulated by rigid links that connect the neighboring segments. The little shell segments that enclose each noodle are not part of this model.

  23. General buckling of starting design (ILINKS=0 or 1 or 2) The noodle support model index, ILINKS, does not affect general buckling because the noodle gap segments are not present in the general buckling model.

  24. Weight versus design iterations during a SUPEROPT execution

  25. Optimization of nasatruss3 with ILINKS = 0

  26. Optimization of nasatruss3 with ILINKS = 2

  27. Optimization of nasatruss3 with ILINKS = 1

  28. Design sensitivity of nasatruss3 optimized with ILINKS = 0 Optimized HEIGHT = 0.58772 inches

  29. Close-up view of STAGS model for local buckling automatically generated by GENOPT/BIGBOSOR4

  30. Another view of STAGS model for local buckling automatically generated by GENOPT/BIGBOSOR4

  31. A view of STAGS model for general buckling automatically generated by GENOPT/BIGBOSOR4

  32. A close-up view of STAGS model for general buckling automatically generated by GENOPT/BIGBOSOR4

  33. General buckling from a STAGS model automatically generated by GENOPT/BIGBOSOR4

  34. Conclusions • GENOPT/BIGBOSOR4 can be used to find minimum-weight designs of axially compressed cylindrical shells with a composite truss-core sandwich wall. • Critical design margins at the optimum are local buckling, general buckling, compressive stress along fibers, and in-plane shear stress. • The effects of “noodles” and “noodle gaps” are significant for local buckling. • Thermal curing has a significant effect on the stress normal to the fibers. • A factor of safety of 1.3 is used for local buckling in the GENOPT/BIGBOSOR4 model in order to compensate for the effects of local transverse shear deformation (t.s.d.) and local shell wall anisotropy, neither of which can be handled by BIGBOSOR4. • Various “noodle support” models (ILINKS=0,1,2) are used for local buckling. It is probably best first to optimize with ILINKS=0 (noodles do NOT support the little shell segments that enclose them), a conservative model, then follow with an investigation with the use of ILINKS = 1 and ILINKS = 2. • The global t.s.d. effect and global anisotropy effect are automatically included in the general buckling models because each of the little shell segments of the truss-core sandwich wall is modeled as a flexible shell segment. There is no “smearing” of properties of the truss-core sandwich wall for general buckling.

  35. The following slides give STAGS predictions These STAGS results are not to be shown with this paper at the 52nd AIAA structures meeting, but may be included among the slides shown by Andrew Lovejoy at that meeting if he wishes to include any of them with his paper. The following slides are from the five supplemental reports: trusscomp.sup.docx, nasatruss2.sup.docx, nasatruss3.sup.docx, isotruss.sup.docx, and isotruss2.sup.docx.

  36. STAGS general buckling spurious mode (Fig. nasatruss2.s1) STAGS finite element 410

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