Titlebook: One-Dimensional Finite Elements; An Introduction To T Markus Merkel,Andreas Öchsner Book 20231st edition Springer-Verlag GmbH Germany, part

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Motivation for the Finite Element Method,ifferent formulations result, which, however, lead to the common principal equation of the finite element method. The forms of description are presented in detail starting from.The finite element method is used to solve various physical problems. Only finite element formulations for structural mecha

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Analogies to the Tension Bar,idered, the designs for torsion are limited to circular cross-sections. In the context of thermoelasticity, cases are considered in which the thermal and elastic behavior are decoupled from each other; for the elastic analysis, the known temperature field is introduced as an additional load.

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Bending Element,t used in this chapter is distinguished from other formulations. The basic equations from strength theory, that is, kinematics, equilibrium and the material law, are introduced and used to derive the differential equation of the bending line. Analytical solutions conclude the basic part. Subsequentl

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General 1D Element,can be obtained for a general 1D element. The stiffness relations of the basic types serve as a basis. For “simple” loading, the three basic types can be considered separately and simply superimposed. There is no interdependence. The generality of the 1D element also applies to arbitrary orientation

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Plane and Spatial Framestructures,other at coupling points. The structure is suitably supported and subjected to loads. The deformations of the structure and the reaction forces at the supports are sought. In addition, the stresses inside the individual elements are of interest. The stiffness relations of the individual elements are

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Plasticity,e yield condition, the flow rule, the hardening law and the elasto-plastic modulus are introduced for uniaxial, monotonic loading conditions. In the context of hardening, the description is limited to isotropic hardening, which occurs, for example, in the uniaxial tensile test with monotonic loading