Physically, one can understand that the element stiffness of a beam decreases in axial compression load and increases in an axial traction load.

Essentially, it is due to the second order term of strain and in compression result in diminishing the total stiffness Ktotal when increasing the geometric stiffness by P*Kg, as Ktotal=(K+P*Kg).Critical loads Pcr are P such that det (K+P*Kg)=0 (where P0).

So, for certain loads it is possible to have geometric stiffness Kg cancelling the classical stiffness K (and it can also be mixed with inertia effects,etc).

Please explain more your question

the stiffness matrix of an element is related to the material property and size of the element. if the stress of the element is below the yield stress, the stiffness is constant and doesn't change with increasing the applied load (because the young modulus is constant). but if yielding happens in an specific element, it's stiffness matrix will change in each time increment. this is due to change of the D matrix in plastic region.

for more details you can read this article.

http://www.sciencedirect.com/science/article/pii/0020740368900015

Dear Dr.Nazar,

It meant by the element stiffness is flexural or bending stiffness of a beam. This stiffness is mathematically reduced when applying an axial external comressive load as its produced a secondary negative action on it.

Thankyou for kind interest.

Thank you Dear Mr.Majid,

Thank you

Physically, one can understand that the element stiffness of a beam decreases in axial compression load and increases in an axial traction load.

Essentially, it is due to the second order term of strain and in compression result in diminishing the total stiffness Ktotal when increasing the geometric stiffness by P*Kg, as Ktotal=(K+P*Kg).Critical loads Pcr are P such that det (K+P*Kg)=0 (where P0).

So, for certain loads it is possible to have geometric stiffness Kg cancelling the classical stiffness K (and it can also be mixed with inertia effects,etc).

Thankyou Dr.Miguel for valuable explanation.

@ Majid Moghaddam

I like to put this comment on your note that stiffness is a structure property, it is not material property.

Sincerely,

B

Thank you Dr. Behzad for kind comment,

Regards