wikifemfuchde2019:lez_2019-06-03
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wikifemfuchde2019:lez_2019-06-03 [2019/06/03 12:41] – [Flexural-torsional buckling example] ebertocchi | wikifemfuchde2019:lez_2019-06-03 [2019/06/05 15:18] (versione attuale) – [Rollbar-like frame structure, o.o.plane transverse load] wikipaom-reviewer | ||
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+ | mentat2013.1 -ogl -glflush | ||
+ | |||
+ | ====== Damped harmonic response ====== | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | How to set a damped response | ||
+ | |||
+ | In order to include a small degree of structural damping (eg. 1% of the critical value) into a MSC.Marc/ | ||
+ | * enter the menu '' | ||
+ | * preemptively define a modulating table 1/ω | ||
+ | * menu '' | ||
+ | * define '' | ||
+ | * set // | ||
+ | * define //table// through '' | ||
+ | * go back to '' | ||
+ | * select the various model materials, and for each of them enter the submenu '' | ||
+ | * leave alone the '' | ||
+ | * define a '' | ||
+ | * set a frequency modulating function, namely //TABLE//, by hitting the '' | ||
+ | * select the just defined '' | ||
+ | * in this way, I defined damping as a function of the $\alpha$ e $\beta$ coefficients introduced by the Rayleigh proportional damping model, with zero $\alpha$ and hence no contribution of the mass matrix. In particular $\zeta = \frac{1}{2}(\frac{\alpha}{2 \pi f}+2 \pi f \beta)$ with $\alpha=0$ and $\beta= 0.01 \cdot g(f)=\frac{0.01}{\pi f}$, from which $\zeta=0.01$ as desired. | ||
+ | * enter the '' | ||
+ | * enter the job '' | ||
+ | * Enter the '' | ||
+ | * substitute them with the //AVAILABLE ELEMENT SCALARS// | ||
+ | * '' | ||
+ | * '' | ||
+ | * the //REAL HARMONIC// e //IMAG HARMONIC// stress resultant equivalents for the beam elements, '' | ||
+ | * insert from the //AVAILABLE ELEMENT TENSORS// block | ||
+ | * '' | ||
+ | * '' | ||
+ | * run the simulation as usual with '' | ||
+ | * open the post file as usual with '' | ||
+ | * The deformed shape may be visualized //according to a given phase// within the oscillation cycle (see also the '' | ||
+ | * Please note that the real component has a 0° phase ($\cos(\omega t)$ modulation) whereas the imaginary component has a 270° phae ($-\sin(\omega t)$ modulation). | ||
+ | * Please also note that in resonance conditions the **imaginary component** becomes dominant and reaches the peak values, whereas the real component vanishes (resonant response is in fact ~90° out of phase with respect to the real, 0° excitation). | ||
+ | * Lets e.g. collect the displacement in $z$ direction of the node at the center of the excited wheel contact area: | ||
+ | * enter the POSTPROCESSING '' | ||
+ | * define the locations for the response sampling with '' | ||
+ | * define the range of the sub-increments to be collected with '' | ||
+ | * proceed with the definition of collected response diagrams by entering th '' | ||
+ | * By hitting '' | ||
+ | * response peaks are now finite (they were theoretically unbounded in the absence of damping), and peaks disappear in correspondence of natural modes that are weakly coupled with the exciting force. In the absence of damping, bounded response at resonance is obtained for **strictly uncoupled** natural modes only. | ||
+ | |||
+ | |||
+ | ====== Euler column buckling ====== | ||
+ | |||
+ | base model: {{ : | ||
+ | |||
+ | buckling load evaluation: {{ : | ||
+ | |||
+ | model at the end of today' | ||
+ | |||
+ | ====== Flexural-torsional buckling example ====== | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | profile made in s235jr steel | ||
+ | |||
+ | thickness: | ||
+ | {{tablelayout? | ||
+ | ^ ^ thickness | ||
+ | | flanges | ||
+ | | web | 2mm | | ||
+ | | gusset plates at supports | ||
+ | |||
+ | simply supported at gusset plate - lower flange intersection nodes ('' | ||
+ | |||
+ | |||
+ | 100kN load, uniformly distributed along the intersection line between the upper flange and the web spanning from support to supports ('' | ||
+ | Please note that in MSC.Marc the supplied point load value is applied to **each** associated node. | ||
+ | |||
+ | Evaluate the peak equivalent von Mises stress along the structure according to the linear elastic modeling. | ||
+ | |||
+ | Due to the compressive state of the profile web, a check with respect to buckling is also required. | ||
+ | |||
+ | ====== a few notes ====== | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | ====== Exam like exercises ====== | ||
+ | |||
+ | ===== Tubolar welded T-joint ===== | ||
+ | The mesh elements are created along the midsurface | ||
+ | * Aluminum (E=70000 MPa, nu=0.3, rho=2.7e-9 tonn/mm^3) | ||
+ | * Chord: | ||
+ | * average diameter: 50mm | ||
+ | * wall thickness: 4mm | ||
+ | * Brace: | ||
+ | * average diameter: 40mm | ||
+ | * wall thickness: 2mm | ||
+ | |||
+ | apply a torsional moment passing through the chord s.t. the nominal shear stress according to the beam theory is 1 MPa; evaluate the stress concentration at the joint as the peak equivalent von Mises stress (according to the employed discretization). | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | ===== Rollbar-like frame structure, o.o.plane transverse load ===== | ||
+ | |||
+ | {{: | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | Find the reaction force $V_\mathrm{A}$ and the reaction moments $\Phi_\mathrm{A}, | ||
+ | |||
+ | Numerically evaluate the unknown quantities with respect to the following dimensions | ||
+ | < | ||
+ | dim: [ | ||
+ | a=800, | ||
+ | b=1000, | ||
+ | E=210000, | ||
+ | G=210000/ | ||
+ | J=(40^4-36^4)*%pi/ | ||
+ | Kt=(40^4-36^4)*%pi/ | ||
+ | ]; | ||
+ | </ | ||
+ | |||
+ | Solution: {{ : | ||
+ | |||
+ | ---- | ||