Good day! I am a beginner in Finite Element Analysis and Structural Mechanics. I have problem in understanding the insight of potential energy approach to derive spring element equations. I have already search for similar post and I found this, and agree with the example raise. https://www.physicsforums.com/showthread.php?t=472249 But I still have problem in applying it to FEA spring element. In the text, total potential energy is defined as the sum of the internal strain energy U and potential energy of the external forces Ω. I.e. ∏p = U + Ω U = 1/2 kx2, this make perfect sense. When we press/pull the spring to x, we give out that amount of energy and the spring is ready to give it back when we release the forces. Energy is conserved. but then I have a difficulties in understanding Ω , I quote the original text: "The potential energy of the externl force, being opposite in sign from the external work expression because the potential energy of the external force is lost when the work is done by external force, is given by Ω = -Fx" My questions are: 1. isn't Ω = - ∑ δF δx ? which is also equal to U? 2.If we substitube F by kx , ∏p = 1/2 kx2 - kx2 = -1/2 kx2, a negative potentia energy? I am very confuse here. I hope somebody can help.