Geometrically Nonlinear Spatial Beam Theory

In real life many structures undergo largedeformation staying in linearly elastic regime.Objective of this book is to study the response ofspatial beams under arbitrary loading where strainremains small. Large local rotation is an essentialpart of the formulation. Beam model has been chosenas the Euler-Bernoulli beam theory and Timoshenkotype first order shear flexible beam. Stretching ofthe reference line and the uniform torsion warpingare being included in the formulation. Jaumann Strainand Stress have been used to circumvent the problemarises due to the use of constant elastic modulus. Areduced stiffness matrix has been derived foranisotropic material. Nonlinear finite element methodis employed to solve the system of ODE.Differentnumerical techniques to solve nonlinear system ofequations have been talked about. To capturepost-buckling behavior, a path following arc-lengthmethod has been used. At the endthe formulation is validated with the existingresults and other numerical experiments are carriedout to demonstrate the workability of the formulationto capture the physics of the problem.