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I'm searching for software which can solve problems regarding engineering mechanics, it will be perfect if it can solve statics, kinematics, dynamics and material mechanics.

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Have you tried Matlab? It has add-ons for most fields of engineering. It was designed to be a working environment for engineers. It is not cheap. The basic package is but add-ons can be expensive. There is a free option called Octave. An open source version of Matlab. I don't know the status of add-ons for Octave. Matlab is developed by Mathworks and has a large user community. If you need an open source solution I'd look into what add-on packages are available with Octave.

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Considering you tagged this question "open-source" you might consider Python scripting with NumPy, SciPy, and Matplotlib.

https://www.google.com/search?q=NumPy+for+mechanical+engineering&ie=utf-8&oe=utf-8

Professional/paid solutions include Mathematica and Maple.

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