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If you think viscoelastic as stress = E(t)*strain, then modulus will change from E(0) to E(t=infinity) (we can think stress relaxation)...then E(0) is instantaneous modulus, E(t=infinity) is called long term modulus.

well, I am not that much familar with anisotropic analytical solution...but by quick searching, I can easily find the following paper, Jinghui Zhang, New analytical free vibration solutions of orthotropic rectangular thin plates using generalized integral transformation...maybe it could be sort of start point for you!

@@Ahn.Eng. Thank you! I will surely check it out !

well..., you can just draw thick wall sphere geometry in your sketch step because we use the axisymmetric modeling in this vedio...that's all^^

Well, I don't have any expertise in this industrial threads and nuts....but, if you compress an axial bar with axially equally distributed friction force (just imagine the similar situation) to the flat surface (bolt head), first thought will be equally distributed axial strain (stress), but the second thought will be ... there might be stress concentration at the flat surface (because it is elastic) and the bottom part of axial bar and internal threads (it will expand/contract in radial direction by Poisson ratio. it will gradually increase in axial direction...it's right....just based on arithmetic ). This is just my initial guess...I hope this can help you~!

@@Ahn.Eng., thank you very much!

I can't check the code in matlab right now....but probably the following code will work! --------------------------------------------------------------------------------------------------------------------------------------------- a = 1.0 r1 = linspace(1,10,400) th1 = linspace(0,2*np.pi,400) r,th = meshgrid(r1,th1) s_inf = 1.0 s_r,s_th,s_rth = stress_holeinplate(r,th,a,s_inf) x = r .* cos(th) y = r .* sin(th) contourf(x,y,s_th,10) For your reference, my original python code for this work is like this ------------------------------------------------------------------------------------------------------------- a = 1.0 # hole radius r1 = np.linspace(1,10,400) # polar coordinate - r th1 = np.linspace(0,2*np.pi,400) # polar coordinate - theta [radian] r,th = np.meshgrid(r1,th1) s_inf = 1.0 s_r,s_th,s_rth = stress_holeinplate(r,th,a,s_inf) x = r * np.cos(th) y = r * np.sin(th) fig = plt.figure() ax = plt.subplot() ax.contour(x,y,s_th,20,colors='black',linewidths=0.1) cax = ax.contourf(x,y,s_th,200,cmap=plt.cm.jet) plt.title(r'Stress Distribution ($\sigma_{\theta}$) - Hole in Infinite Plate') ax.set_xlabel(' X ') ax.set_ylabel(' Y ') plt.xlim(-5,5) plt.ylim(-5,5) ax.set_aspect('equal') fig.colorbar(cax) plt.show()

@@Ahn.Eng. could you please share the full code with us?

Well,..I think you could model it as the following 3 ways!? 1) Import Sketch File (such as *.igs) which has exact varying thickness dimension 2) Compute xy coordinates of varying thickness and just make a model using “create spline:through points” sketch option 3) Just make a model using “axisymmetric/deformable/wire” instead of "shell" and then create varying thickness using “shell thickness: nodal distribution” option in Edit Section

Well,..I think you can do this way.. (1) you can assign "constraints/rigidy body" option for the plate instead of cylinder. (2) or when selecting part type at the beginning, just select "Analytical rigid" instead of usual "Deformable" for the plate. I hope this's helpful for you ~

I used nonlinear geometry option on and CPE8 element type (An 8-node biquadratic plane strain quadrilateral)~

I guess, you can try to adjust your initial time step or minimum time step...or (2) check your contact situation (initial gap?...)... or (3) you could try to use stabilization options... I think, the following blog could be great help for you. info.simuleon.com/blog/6-tips-solving-non-convergence-with-abaqus-fea

I think, it should be the same if your FE model has enough number of elements numbers and beam aspect ratio (length vs. section area). Solver choice?

Well, I'm not sure problem definition(random inter-particle distance of particles?, particle density in a volume?) because I am not familiar with that topic. However, if you can define particle features (in term of movement,.etc.), then you can do monte carlo simulation. Please more hints or specific information~. Thanks.

You can download Figure calibration (download from (1), general explanation from(2)) (1) www.astro.physik.uni-goettingen.de/~hessman/ImageJ/Figure_Calibration/ (2) lukemiller.org/index.php/2011/09/digitizing-data-from-old-figures-with-imagej/