Serial number

Judgment and instruction

The situation of BC. satisfied in examples

BC.1

(for y)

For both Lever 1 and Lever 2, there is displacement on the free top, but there is not on the fixed bottom.

It is satisfied in all the methods of example 1 and 2.

BC.2 (for or)

For both Lever 1 and Lever 2, there is angular rotation on the free top, yet there is not on the fixed bottom.

It is satisfied in all the methods of example 1 and 2

BC.3 (for or m)

For both Lever 1 and Lever 2, there is no moment at the top but there is on the bottom.

It is satisfied in all the methods in example 1 and 2

BC.4 (for or S); S exists on the sections where the load direction isn’t parallel to the shaft only

For Lever 1, there is for the direction of the load is not parallel to the shaft on the top; yet on the bottom as they are parallel to each other.

For this BC. is only satisfied partly in method 1 and 2, the accuracy is not so good; yet in method 3 - 6, the BC.s is satisfied completely, making the accuracy very high.

For Lever 2, as there is no load on the top, there is no shear there; yet on the bottom section, there is no shear either for the shaft is parallel to the direction of the loads.

For methods 3 - 10 in example 2, as the fist 4 BC.s are all satisfied completely, the accuracies are very high.

BC.5 (for or: the simulation distributed load being different from the own weight of q)

For Lever 1, as ; As then.

In example 1, method 5, 6 satisfies all the first 5 BC: s the accuracies are very high.

For Lever 2, there as the load direction being not parallel to the shaft; either as function of m is changing with the shaft not to scale of z.

All the first 5 BC.s have been satisfied in method 5 - 10 in example 2:, they all have a good precision.

BC.6 (for or)

For Lever 1, this condition comes from method 4 in example 1.

Method 6 in example 1 satisfied all the first 6 BC.s, the precision is the highest

For Lever 2, it is difficult to determine the exact value of, yet is easy to be determined for the situation similar to the uniformly distributed load acting on the free end of a beam. So function m is very complicated, it means, then verified by example 2.

As all the 7 BC.s are satisfied in method 5 - 10 in example 2, the accuracy is very high.

BC.7 (for Lever 2 only)

Pre-judging

For and; as is very small, then is prejudged in example 2

Actually is about 2.4

As the accuracy of method 9 in example 2 is the highest, is clear.

Supplement (for Lever 1 only)

If n is an uneven integer

All the methods in example 1 are satisfied

If n is an even integer