Stiffness of Trianglated Beam Shell structure Calculation

Replies to This Discussion

Permalink Reply by Karamba3D on October 31, 2016 at 1:15pm

Dear Lei,

it is possible to combine beam- and shell elements in Karamba.

What do you mean by 'check the stiffness'? Calculate the maximum displacement or the eigenfrequency?

Best,

Clemens

Permalink Reply by Lei Yang on November 2, 2016 at 12:33am

Dear Clemens,

Thank you for the reply.

By saying 'check the stiffness', I mean, the value of stiffness which by general structural understanding is the ability against bending distrotion.  Can I say in a Trianglated Beam system, the smaller value of Displacement, the better stiffness of the structure?

Thank you so much

Best,

Lei

Permalink Reply by Karamba3D on November 2, 2016 at 1:23am

Dear Lei,

the stiffness of a structure is a global property which can be quantified in different ways:

• The maximum displacement can be used as an indicator, depends however on the applied load and may be governed by a few single weak points of a structure.
• The internal energy (see output-plug 'Energy' on the Analysis-component) also depends on the external loads but is a more global meassure of stiffness.
• Another indicator of stiffness is the Eigenvalue of the stiffness matrix. This value is independent of external loads and offers a good basis for comparing structural alternatives in e.g. an optimization.
• The Eigenfrequency gives a global meassure of stiffness independent of external loads and takes into account the distribution of mass.

The smaller the value of the above properties the stiffer the structure.

In case of grid shells instability may be a governing factor. In this case the buckling load factor would be better suited to judge the load bearing capacity of the structure (see manual) as the properties mentioned above.

Best,

Clemens

Permalink Reply by Lei Yang on November 2, 2016 at 3:13am

Dear Clemens,

Thank you so much again!

In case of form finding and optimization at the begining of design process, Are you suggesting use the 'Energy' out-put as the 'stiffness' check value to run a GA simulation?

I`m thinking at the begining just use the mass weight as the load, no external loads for now. So i turn MaxUtil value to 0.7. don`t if that is appropriate?

Besides, are there any outputs that I could get the value of 'Eigenvalue of the stiffness matrix' and 'Eigenfrequency'?

Thank you so much!

Love Karamba.

Best Regards,

Lei

Permalink Reply by Karamba3D on November 2, 2016 at 1:27pm

Dear Lei,

the proper choice of the objective function depends on what you want to optimize. If you want to find the best position of supports for a structure that is given, the internal energy output is a good choice since it can be determined fast.

For more involved problems where the structure itself changes appreciably the mass after cross section optimization would be a better indicator. The 'Cross Section Optimizer'-component makes sure that the structure is strong enough (i.e. satisfies the ultimat limit criteria) and usable (by limiting the maximum displacement).  For details see the manual. It takes however much more time to compute. You can use the Grasshopper profiler to meassure the runtime.

Working with dead weight as the only external load complicates the optimization when the volume of the structure can change. Whether it is a good idea to use dead weight only depends on the ration between dead and live load. Usually it is better to include both.

The first Eigenvalue of the stiffness matrix can be calculated with the 'Eigen Modes'-component, the first Eigenfrequency with the 'Natural Fibrations'-component.

Best,

Clemens

Permalink Reply by Lei Yang on November 3, 2016 at 3:55am

Dear Clemens,

Thank you again and again, infinite loop..

The 'Internal Energy Out-put' from 'OptiCrosSec' component, Can i understand this option as the ability to absorb energy where distortion happens? Hence, The larger value of energy out-put, the better stiffness of the structure?

Thank you so much.

Best,

Lei

Permalink Reply by Karamba3D on November 3, 2016 at 2:52pm

Dear Lei,

no, it's the other way round: the smaller the intake of elastic energy under a specific set of loads the stiffer the structure (see the manual for more details).

Best,

Clemens

Permalink Reply by Lei Yang on November 6, 2016 at 8:52pm

Dear Clemens,

Thanks so much!

Best wishes,

Lei

Permalink Reply by Karamba3D on October 2, 2017 at 12:45pm

Dear all,

I made a mistake here:

it is true that the smaller the maximum displacement and the internal energy under given loads the stiffer the structure.

For the first Eigenvalue of the stiffness matrix and the Eigenfrequency this is not correct. It is the other way round: The larger the first eigenvalue of the stiffness matrix and the first natural frequency the stiffer the structure.

Best,

Clemens