Advanced Topics, Volume 2, Non-Linear Finite Element by M. A. Crisfield

By M. A. Crisfield

Non-linear Finite point research of Solids and buildings quantity 2: complicated issues M. A. Crisfield Imperial collage of technological know-how, expertise and drugs, London, united kingdom In such fields as aeronautical, civil, mechanical and structural engineering, non-linear research suggestions have gotten familiar for the answer of sensible engineering difficulties. Taking an engineering instead of a mathematical bias, this finished booklet builds at the primary principles defined in quantity One, introducing the reader to extra special, complex themes. huge traces and big rotations, plasticity with various yield standards and hardening ideas, balance thought and complicated resolution approaches together with branch-switching recommendations, touch and friction, and nonlinear dynamics, are lined intensive. Examples from a non-linear finite point laptop application incorporating the complicated answer systems are incorporated. the pc application is on the market on the net through nameless ftp, utilizing the URL ftp://ftp.cc.ic.ac.uk/pub/depts/aero/nonlin2/.

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Additional info for Advanced Topics, Volume 2, Non-Linear Finite Element Analysis of Solids and Structures

Example text

An alternative that is often adopted in large-strain analysis is to relate all measures to the current configuration. 2. McMeeking and Rice called this approach ‘Eulerian’ and used it for large-strain elasto-plastic analysis. The details of the elasto-plastic side of the analysis will be discussed in Chapter 19 (with the related topic of hyperelasticity being considered at an earlier stage in Chapter 13). For the present we will concentrate on the development of the finite element equations-in particular the internal force vector and the tangent stiffness matrix.

The previous conditions can be expressed as . 3) we have introduced the notation that will be used throughout this chapter whereby a dot is used for the 'dot product' rather than using the transpose symbol, 'T'. 4) where is the volume of the parallelepiped with edges along the base vectors ei. 5) A n y vector, can now be expressed either in terms of the (global) orthonormal base vectors i , - i 3 or the base vectors e , -e3 or the reciprocal base vectors, e'-e3. 6b) are known as the covariant components of x.

In the current ‘Eulerian procedure’ the progress of a specific material particle is traced and in that sense the method is Lagrangian. Indeed it could be termed as a form of updated Lagrangian technique whereby the referenceconfiguration is the current configuration. 4). In contrast in our Eulerian formulation, the reference configuration is continuously changing and we must account for this change. 3 and Chapter 13), the Eulerian formulation can be exactly equivalent to one based on the Green strain and second Piola-Kirchhoff stresses using the total Lagrangian approach.

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