Hirad Assimi

• PhD Candidate
• PhD Student at The University of Adelaide

I tried to model a simply supported bridge, but I can't reproduce the results in the literature. The description of the truss is as follows,

"To demonstrate the flexibility of the approach, a simply supported bridge is optimized for its weight minimization with several cases of frequency constraints. Members on the lower chord are represented by beam elements with fixed rectangular cross sections B = 8 cm and H = 5 cm. Others are modeled as bar elements with initial sectional areas A = 1 cm2 . Young’s modulus is E = 2.1 × 1011 Pa, and the material density is ρ = 7800 kg/m3 for all elements. The initial configuration of the structure is shown in Fig. 6. A nonstructural mass m = 10 kg is attached at each of the nodes on the lower chord. The natural frequencies of the truss are about 20, 40 and 60" with some variations in the third or fourth floating point.

The schematic of the truss is depicted is attached.

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First I modeled all elements as bar elements and it resulted in natural frequencies as "20.35 40.00 60.27". I believe that It came to a correct K matrix but the M matrix somehow was wrong. I surveyed the literature and I found out that the lower chord elements should be beam elements and I modified my model. But it still gives me very wrong Frequencies that are mentioned at the end. I also supposed that Iz in the beam element command of OpenSEES should be (bh/12)*(b^2+h^2) and consistent mass matrix as (rho*cross-section). I will appreciate if you help me to modify the model to repeat the literature results.

My tcl code is as follows and also attached:

Result of the code:

I want to obtain the natural frequencies of a benchmark truss which is famously known as the ten-bar planar truss. It consists of 10 truss members and 6 nodes. Two nodes are its supports and other four nodes are free nodes. The modulus elasticity is 6.89e10 and the added non-structural mass to the free nodes is 454 kg. Fig 1 shows the schematic of the truss and the obtained cross-section areas of this problem is listed in Fig 2. This figure also lists the natural frequencies obtained by different trusses. I tried to simulate the truss obtained by MC-TLBO which is listed in the last column but I faced a problem:

I didn’t reach the natural frequency in the literature and my model resulted in omega^2=1.575894e+04 and f=(omega/(2*pi))=19.98 Hz. It’s notable that I added some negligible massed on the other degree of freedom of the nodes according to OpenSEES official examples to obtain other natural frequencies.

The figures are referred from the [1] and The Tcl model is attached by myself (The units are in SI).

Any comment will be appreciated and thanks in advance for your time.

Refs.

[1] Farshchin, M., C. V. Camp, and M. Maniat. "Multi-class teaching–learning-based optimization for truss design with frequency constraints." Engineering Structures 106 (2016): 355-369.

I'm trying to model a 25 bar truss benchmark with elastic elements but the loading is somehow weird to me. Can you tell me what kind of loading it's ? Those multiple force vectors on nodes 1 and 2 are applied simultaneously or else? Why the resultant forces can not be considered? The schematic of the 25 bar truss and the loading conditions are attached.

Any comment would be appreciated. Thx in advance

sources of attached materials:

Cheng, Min-Yuan, Doddy Prayogo, Yu-Wei Wu, and Martin Marcellinus Lukito. "A Hybrid Harmony Search algorithm for discrete sizing optimization of truss structure." Automation in Construction 69 (2016): 21-33.

I want to model this 25 bar truss benchmark. the schematic of the benchmark, the loading conditions and my partial tcl file are attached.

How can I define this kind of loading in my code? Because there are multiple loading on nodes 1 and 2.

is it possible with multiple pattern plains? if yes how can i link them to analyze simultaneously.

I tried to model it as it's shown in the tcl file, but it doesn't work, since the  maximum deflection in the nodes should be lower than 0.35 inch.

Any help would be appreciated, thanks in advance.

source of pictures : http://ethesys.lib.ttu.edu.tw/ETD-db/ETD-search/getfile?URN=etd-0813110-182801&filename=etd-0813110-182801.pdf

The features which I'm looking for are powerful library of elements and materials like Opensees, having various solvers, handling static/dynamic loading/analysis and capability of running in command-line platform (console) to make it easy to link.