Does there exist software to test the strength of a designed LEGO model?
First step, have you read my paper? This should give you a good guide on what is the maximum force needed to break Lego.

With these limits in mind, the next thing to note is that breaking doesn't equal bending. Lego will bend quite a lot before breaking so designing structures that a rigid will basically meet most requirements.

The best book to read is Sariel's Technic Builders Guide. This outlines a number of design patterns that maximize strength.

In general, you should think of Lego as weak steel. Triangles everywhere and vertical plates.