Calculating displacement of variable force
the problem of beam deformation or displacement is very simple to understand with karnoky's theorem. However, when I studied mechanics of materials, I turned over several books and didn't introce them in detail. Maybe it's not right. I won't introce them in detail here. I found a tutorial website for you, You can also find related tutorials on the Internet by yourself, in which you need to use some knowledge of advanced mathematics.
http://wlxt.whut.e.cn/cllx/cllx_ web/pages.asp?c=11&s=4
definition of work: the proct of the force on an object and the displacement in the direction of the force
in the same direction: a = f * D
in general: a = f * D * cos θ
it's actually the proct of vectors F and D.
1. The definition is different. Displacement is a vector, which refers to the linear distance along the direction of force or along the direction of member. Deformation generally refers to bending deformation, torsion deformation, tension compression deformation, etc. Strain is the unit of deformation, the deformation in a very small size
2. The object of displacement research is usually a point in the structure. The research object of deformation is usually the whole member or other single integral member. The object of strain study is the dense particles inside the bar
The calculation method is different. Each has its own formula. For linear elastic materials, the strain is directly proportional to the stress, and the proportional coefficient is the elastic molus E The relationship among the three is that they are all descriptions of the physical changes of members under the action of force The stability of the material is generally for the compression bar, so it is usually called the compression bar stability problem, which means that the compression bar loses stability before reaching the strength condition. There are Euler formula (large flexibility), straight line formula, parabola formula, etc 
extended data:
1. The problem of beam deformation calculation was proposed by nemore J de as early as the 13th century, and has been studied by Jacobs Bernoulli, Daniel Bernoulli and Euler L
In 1826, Navier obtained the correct differential equation of deflection curve and the correct formula of bending strength of beam in his lectures on mechanics of materials, which laid a correct theoretical foundation for the calculation of deformation and strength of beam Russian railway engineer rulavsky ЖуравскийДИ In 1855, the shear stress formula for transverse bending was obtained. Thirty years later, his compatriot besparov ВеспаловД He is considered to be the first person to use bending moment diagram in history