New developments in structural optimization using optimality criteria:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Düsseldorf
VDI-Verl.
1996
|
| Edition: | Als Ms. gedr. |
| Series: | Verein Deutscher Ingenieure: [Fortschritt-Berichte VDI / 18
199 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 162 S.: graph. Darst. |
| ISBN: | 3183199181 |
Staff View
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Record in the Search Index
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| adam_text | Titel: New developments in structural optimization using optimality criteria
Autor: Birker, Torben
Jahr: 1996
SCHRITT- m BERICHTElf IjI M. Sc. Torben Birker, Essen New Developments in Structural Optimization Using Optimality Criteria Reihe 18 : Mechanik/ Bruchmechanik Nr. 199 VW VERLAG
IV Table of contents Acknowledgements ............................................................. HI Table of contents............................................................... IV Notation.......................................................................VIII Abstract........................................................................ X Introduction.................................................................... 1 1 Least-weight trusses with displacement constraints..................... 4 1.1 Problem formulation and notation....................................... 5 1.2 Solution for one active displacement constraint........................... 8 1.2.1 Feasible regions for the cost function Wj ........................... 10 1.2.2 Solution for one active compliance constraint - special case........ 11 1.3 Solution for two active displacement constraints.......................... 12 1.3.1 Feasible regions for the cost function Wj k .......................... 13 1.4 Relations between the weight functions Wj and W jk ...................... 13 1.5 Illustrative examples of optimal layouts for two-bar trusses............... 14 1.5.1 Optimal solution with one active displacement constraint.......... 14 1.5.2 Optimal solution with two active displacement constraints......... 18 1.6 Exact optimal solution using optimality criteria.......................... 21 1.6.1 Optimality criteria for a discretized solution....................... 21 1.6.2 Optimality criteria for a continuum-type solution.................. 24 1.7 Illustrative examples of exact least-weight trusses......................... 26 1.7.1 Exact optimal solution for one active displacement constraint...... 26 1.7.2 Exact optimal solution for two active displacement constraints..... 29 1.7.3 Evaluation of the results.......................................... 31 1.8 Concluding remarks..................................................... 34 2
Least-weight trusses with combined displacement and stress constraints 35 2.1 Problem formulation and notation....................................... 35 2.2 Solution for active displacement constraint............................... 37
Table of contents V 2.2.1 Feasible regions for the cost function W x ........................... 38 2.3 Solution for active displacement and stress constraints.................... 38 2.3.1 Feasible regions for the cost function W la .......................... 39 2.3.2 Solution for active displacement and stress in “b”-bar constraints .. 40 2.4 Solution for active stress constraints...................................... 41 2.4.1 Feasible regions for the cost function W ab .......................... 42 2.5 Relations between the cost functions VFi, W a , W ib and W ab ............... 42 2.6 Illustrative examples of optimal layouts for two-bar trusses............... 44 2.6.1 Optimal solution with active displacement and stress constraints... 44 2.6.2 Optimal solution with active stress constraints..................... 48 2.7 Exact optimal solution using optimality criteria.......................... 52 2.7.1 Optimality criteria for a discretized solution....................... 52 2.7.2 Optimality criteria for a continuum-type solution.................. 54 2.8 Illustrative examples of exact least-weight trusses......................... 54 2.8.1 Exact optimal solution for combined active constraints............. 55 2.8.2 Exact optimal solution for active stress constraints................. 58 2.8.3 Evaluation of the results.......................................... 58 2.9 Concluding remarks..................................................... 61 3 General formulation of the DCOC method.............................. 66 3.1 Problem formulation..................................................... 66 3.2 Principle of the DCOC method.......................................... 69 3.3 Generalization of the DCOC method..................................... 72 3.4 Problems with several active local constraints............................ 74 3.4.1 The Kreisselmeier-Steinhauser function............................ 76 3.5
Computational solution algorithm........................................ 78 3.5.1 Preprocessing..................................................... 78 3.5.2 Finite element computations...................................... 78 3.5.3 Determination of global Lagrange multipliers...................... 81 3.5.4 Updating of design variables...................................... 83 3.5.5 Convergence check of control regions.............................. 85 3.5.6 Determination of local Lagrange multipliers....................... 85 3.5.7 Convergence check of design variables............................. 86 3.5.8 Postprocessing.................................................... 86 3.6 Concluding remarks..................................................... 86 4 Application to trusses..................................................... 87 4.1 Two-bar least-weight trusses............................................. 87
VI Table of contents 4.1.1 Two-bar truss with one active displacement constraint............. 90 4.1.2 Two-bar truss with two active displacement constraints............ 92 4.1.3 Two-bar truss with active displacement and stress constraints...... 92 4.1.4 Two-bar truss with active stress constraints....................... 94 4.2 Truss layout based on design codes....................................... 94 4.2.1 Requirements according to Eurocode no. 3........................ 95 4.2.2 Truss layout with linear increasing cross-sectional areas............ 97 4.2.3 Truss layout with standardized cross-sectional areas............... 101 4.2.4 Illustrative example: 10-bar truss..................................105 4.2.5 Illustrative example: 31-bar truss..................................107 4.3 Concluding remarks..................................................... 108 5 Application to plane stress plates.........................................Ill 5.1 Problem formulation..................................................... HI 5.2 Affect of element type................................................... 114 5.3 Affect of penalty factor.................................................. 116 5.4 Affect of initial layout................................................... 117 5.5 Concluding remarks..................................................... 119 6 Extensions to other continua ..............................................121 6.1 Application to bending plates............................................ 121 6.1.1 Example: Clamped square plate................................... 125 6.1.2 Example: Simple supported square plate.......................... 126 6.1.3 Example: Simple/free supported square plate...................... 127 6.1.4 Example: Simple/free supported rhombic plate.................... 128 6.2 Application to three-dimensional continua ................................ 129 6.2.1 Illustrative example:
Pyramid..................................... 131 6.2.2 Illustrative example: 3-D beam....................................131 6.3 Concluding remarks..................................................... 132 Conclusions.....................................................................134 Appendices A Lagrange function and Kuhn-Tucker necessary conditions..............136 A.l Lagrange function....................................................... 136 A.2 Kuhn-Tucker necessary conditions....................................... 139 B Optimal bar orientations for two-bar trusses............................141
Table of contents VII B.l Bar angles for a truss with one displacement constraint.................. 141 B. 2 Bar angles for a truss with two displacement constraints................. 144 C Element library.............................................................146 C. l Space truss element..................................................... 146 C.2 Constant strain triangle - plane stress................................... 148 C.3 Isoparametric plane element - plane stress............................... 150 C.4 Isoparametric Mindlin plate element..................................... 153 C.5 Isoparametric solid element.............................................. 155 References......................................................................158
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| spelling | Birker, Torben Verfasser aut New developments in structural optimization using optimality criteria Torben Birker Als Ms. gedr. Düsseldorf VDI-Verl. 1996 X, 162 S.: graph. Darst. txt rdacontent n rdamedia nc rdacarrier Verein Deutscher Ingenieure: [Fortschritt-Berichte VDI / 18 199 Zugl.: Essen, Univ., Diss., 1996 Fachwerk (DE-588)4139209-7 gnd rswk-swf Leichtbau (DE-588)4035165-8 gnd rswk-swf Strukturoptimierung (DE-588)4183811-7 gnd rswk-swf Platte (DE-588)4046304-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Leichtbau (DE-588)4035165-8 s Fachwerk (DE-588)4139209-7 s Strukturoptimierung (DE-588)4183811-7 s DE-604 Platte (DE-588)4046304-7 s 18 Verein Deutscher Ingenieure: [Fortschritt-Berichte VDI 199 (DE-604)BV001902156 199 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007339505&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Birker, Torben New developments in structural optimization using optimality criteria Fachwerk (DE-588)4139209-7 gnd Leichtbau (DE-588)4035165-8 gnd Strukturoptimierung (DE-588)4183811-7 gnd Platte (DE-588)4046304-7 gnd |
| subject_GND | (DE-588)4139209-7 (DE-588)4035165-8 (DE-588)4183811-7 (DE-588)4046304-7 (DE-588)4113937-9 |
| title | New developments in structural optimization using optimality criteria |
| title_auth | New developments in structural optimization using optimality criteria |
| title_exact_search | New developments in structural optimization using optimality criteria |
| title_full | New developments in structural optimization using optimality criteria Torben Birker |
| title_fullStr | New developments in structural optimization using optimality criteria Torben Birker |
| title_full_unstemmed | New developments in structural optimization using optimality criteria Torben Birker |
| title_short | New developments in structural optimization using optimality criteria |
| title_sort | new developments in structural optimization using optimality criteria |
| topic | Fachwerk (DE-588)4139209-7 gnd Leichtbau (DE-588)4035165-8 gnd Strukturoptimierung (DE-588)4183811-7 gnd Platte (DE-588)4046304-7 gnd |
| topic_facet | Fachwerk Leichtbau Strukturoptimierung Platte Hochschulschrift |
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