%0 Journal Article %1 schmidt1977nonlinear %A SCHMIDT, WILLIAM %D 1977 %J Computers and Structures %K BEAMS BENDING NONLINEAR %P 153-158 %T NONLINEAR BENDING OF BEAMS USING THE FINITE ELEMENT METHOD %V 8 %X In this paper a finite element formulation for determining the finite deflection of thin bars is presented. The nonlinear stiffness equations are generated after simple approximate expressions involving the nodal parameters are used to replace the nonlinear terms in the energy functional. The procedure used results in a simplified set of nonlinear algebraic equations which are more amenable to solution than the equations usually presented. The applicability and accuracy of the method together with an evaluation of three incremental solution techniques, a step by step method. a one step Newton-Raphson procedure, and a variable interpolation technique is demonstrated by solving a cantilever beam with a point load acting on the end. Curves showing the sensitivity to increment size and to the number of elements are also presented. The results indicate that the formulation is accurate and inexpensive in terms of computational effort.

@article{schmidt1977nonlinear, abstract = {In this paper a finite element formulation for determining the finite deflection of thin bars is presented. The nonlinear stiffness equations are generated after simple approximate expressions involving the nodal parameters are used to replace the nonlinear terms in the energy functional. The procedure used results in a simplified set of nonlinear algebraic equations which are more amenable to solution than the equations usually presented. The applicability and accuracy of the method together with an evaluation of three incremental solution techniques, a step by step method. a one step Newton-Raphson procedure, and a variable interpolation technique is demonstrated by solving a cantilever beam with a point load acting on the end. Curves showing the sensitivity to increment size and to the number of elements are also presented. The results indicate that the formulation is accurate and inexpensive in terms of computational effort.}, added-at = {2020-06-01T12:41:22.000+0200}, author = {SCHMIDT, WILLIAM}, biburl = {https://www.bibsonomy.org/bibtex/2171565e1ce6d16937c031c60165c23a9/chkokalis}, interhash = {11f93f1fa36095fdcbda0f86dedcb4cc}, intrahash = {171565e1ce6d16937c031c60165c23a9}, journal = {Computers and Structures}, keywords = {BEAMS BENDING NONLINEAR}, pages = {153-158}, timestamp = {2020-06-02T15:37:00.000+0200}, title = {NONLINEAR BENDING OF BEAMS USING THE FINITE ELEMENT METHOD}, volume = 8, year = 1977 }