Part 1 : Modelling. Practical application of the MFE. Method of Finite Elements I. Institute of Structural Engineering Page 1
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1 Institute of Structural Engineering Page 1 Practical application of the MFE Part 1 : Modelling
2 Institute of Structural Engineering Page 2 Goals of this Lecture Demonstrating the importance of modelling when applying the MFE Closing the gap between structural analysis theory and application of FE software Note: In this lecture the focus is on structural engineering
3 Institute of Structural Engineering Page 3 "Structural engineering is the art of molding materials we don't wholly understand, into shapes we can't fully analyze, so as to withstand forces we can't really assess, in such a way that the community at large has no reason to suspect the extent of our ignorance." Structural Engineering = Mission impossible Always keep this in mind when doing advanced FE calculations!
4 Institute of Structural Engineering Page 4 Structural Engineering Physical PROBLEM Analytical SYSTEM Finite Element MODEL Finite Element RESULT Detailed CONSTRUCTION Y X Computational Structural Analysis
5 Institute of Structural Engineering Page 5 Structural Engineering Physical PROBLEM Analytical SYSTEM Finite Element MODEL Finite Element RESULT Detailed CONSTRUCTION Y X Modelling Calculation Detailing engineer computer engineer Note: The computer is playing a minor role!
6 Institute of Structural Engineering Page 6 FE Modelling Physical PROBLEM Analytical SYSTEM Finite Element MODEL Y X Modelling = defining Structure type Analysis type Analytical system Actions e.g. 2D/3D, frame, shell linear statics, nonlinear dynamics nodes, elements, boundary conditions moving load, earthquake
7 Institute of Structural Engineering Page 7 FE Modelling World Mechanical Eng Civil Eng Object Airplane Building Problem Vibrations Cracking Deformations Collapse (FE) Model Analysis Linear dynamics Stresses Structure 3D shell 2.5D slabs 3D frame Linear statics/dynamics Ultimate load
8 Institute of Structural Engineering Page 8 Example: Modelling a Girder Model A Model B Model C??
9 Institute of Structural Engineering Page 9 Modelling Making assumptions based on engineering judgement Building an appropriate, consistent analytical system The (one and only) correct model does not exit Modelling is hard, but the most important step!
10 Institute of Structural Engineering Page 10 Example: Slab on Columns FE Model slab column Best FE model =? FE Model A 2D slab 3 dof/node, bending element linear elastic analysis point support => Stress concentrations at support node!
11 Institute of Structural Engineering Page 11 Example: Slab on Columns FE Model B elastic element support => No clamped support possible! FE Model C 1. Find reactions from point support 2. Add correcting loads: => Best results!
12 Increased complexity Institute of Structural Engineering Page 12 Example: Modelling a Building Physical Problem FE Models 3D shell? 3D frame 2.5D slabs + 3D frame / system of beams
13 Institute of Structural Engineering Page 13 Example: Modelling a Building 2.5 D Model for vertical loads: "Stack of slabs" Start with top story: 1. Upper story: 2D slab analysis => reactions 2. Walls/columns: reaction transfer + dead load => foot reactions 3. Lower story: import reactions as slab loads Storey i Continue to next story and repeat the 3 steps all the way to the foundation. Storey i-1
14 Institute of Structural Engineering Page 14 Example: Modelling a Building Earthquake Analysis?? Equivalent cantilever beam 3D shell 3D frame / system of beams
15 Institute of Structural Engineering Page 15 Model: 3D Shell Good Suitable for any geometry (curved shells..) Nicest result pictures (marketing..) Bad Most detailed model (big input => big output) Verifying the results is extremely demanding Not fully covered by codes Long computing times (=> no sensitivity analysis possible..) No direct results for construction (reinforcement of walls..) Verdict Not suited for engineering practice
16 Institute of Structural Engineering Page 16 Model: 3D Frame Good Based on beam theory (=> result interpretation..) Directly supported by codes Very well covered by literature Suitable for all types of analysis Short computing times (=> sensitivity analysis..) Direct results for construction Bad Cannot model 3D curved shell structures Verdict Best model for engineering practice
17 Institute of Structural Engineering Page 17 The 4 Golden Rules of FE-Modelling 1. Understand the problem before starting the FE software 2. Model the (structural) system not the geometry 3. Unverifiable FE results are generally false 4. Follow the basic system assumptions all the way to the construction
18 Institute of Structural Engineering Page 18
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