Matrix formulation of geometric nonlinearity

In order to incorporate geometric nonlinearity into matrix analysis, a new set of external forces, referred to as second-order forces, ¹ have been introduced. Figure A5.1 illustrates this concept, where a new force F_2order is introduced on the right, acting in conjunction with forces N and V. By including the second-order forces in the external actions, the first-order analysis in the undeformed configuration can be used to obtain second-order internal forces and moments. Figure A5.1 Second-order calculation using second-order forces. A drawing showing two cantilever columns, one with the deformed shape and the other in its original position. There are forces acting on the top of both columns. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003169659/21dba207-18a6-49a1-b5b3-c46a8d6cf2d8/content/figA5_1_PB.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003169659/21dba207-18a6-49a1-b5b3-c46a8d6cf2d8/content/figA5_1_OC.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>