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Unformatted text preview: Transient Dynamic Analysis 42 D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . Module 4 Transient Dynamic Analysis A. Define transient dynamic analysis and its purpose. B. Learn basic terminology and concepts underlying transient analysis. C. Learn how to do a transient analysis in ANSYS. 43 D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . Transient Analysis A. Definition & Purpose What is transient dynamic analysis? • A technique to determine the response of a structure to arbitrary timevarying loads such as an explosion. • Input – Loads as a function of time. • Output – Timevarying displacements and other derived quantities such as stresses and strains. 44 D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . Transient Analysis … Definition & Purpose Transient dynamic analysis is used in the design of: • Structures subjected to shock loads, such as automobile doors and bumpers, building frames, and suspension systems. • Structures subjected to timevarying loads, such as bridges, earth moving equipment, and other machine components. • Household and office equipment subjected to “bumps and bruises,” such as cellular phones, laptop computers, and vacuum cleaners. 45 D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . Transient Analysis B. Terminology & Concepts Topics covered: • Equation of motion • Solution methods • Integration time step 46 D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . Transient Analysis  Terminology & Concepts Equation of Motion • Equation of motion for a transient dynamic analysis is the same as the general equation of motion. • This is the most general form of dynamic analysis. Loading may be any arbitrary function of time. • Depending on the method of solution, ANSYS allows all types of nonlinearities to be included in a transient dynamic analysis  large deformation, contact, plasticity, etc. [ ] { } [ ]{ } [ ]{ } ( ) { } t F u K u C u M = + + & & & 47 D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . Transient Analysis  Terminology and Concepts Solution Methods Solving the equation of motion Direct Integration Mode Superposition Implicit Explicit Full Reduced Full Reduced 48 D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . D Y N A M I C S 7 . Transient Analysis  Terminology and Concepts … Solution Methods Two methods of solving the equation of motion: • Mode superposition • Direct integration – Equation of motion is directly integrated step by step over time. At each time point ( time = 0, Δ t , 2 Δ t, 3 Δ t,….) a set of simultaneous, static equilibrium equations (F=ma) is solved....
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 Spring '09
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