Bending Element

  • Andreas Öchsner
  • Markus Merkel


By this element the basic deformation bending will be described. First, several elementary assumptions for modeling will be introduced and the element used in this chapter will be outlined towards other formulations. The basic equations from the strength of materials, meaning kinematics, equilibrium and constitutive equation will be introduced and used for the derivation of the differential equation of the bending line. Analytical solutions will conclude the section of the basic principles. Subsequently, the bending element will be introduced, according to the common definitions for load and deformation parameters, which are used in the handling of the FE method. The derivation of the stiffness matrix is carried out through various methods and will be described in detail. Besides the simple, prismatic bar with constant cross-section and load on the nodes also variable cross-sections, generalized loads between the nodes and orientation in the plane and the space will be analyzed.


Shape Function Stiffness Matrix Global Coordinate System Bernoulli Beam Finite Element Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of Mechanical Engineering, Department of Applied MechanicsUniversity of Technology Malaysia—UTMSkudaiMalaysia
  2. 2.Department of Mechanical EngineeringAalen University of Applied SciencesAalenGermany

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