By Boresi A.P., Schmidt R.J.
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The spatial coordinates are denoted by x = [x, y]T and the material coordinates by X = [X, Y]T. e. it gives a vector for every pair of the independent variables. 11) In a Lagrangian mesh, the nodes are coincident with material (Lagrangian) points, so for Lagrangian nodes, XI = constant in time For an Eulerian mesh, the nodes are coincident with spatial (Eulerian) points, so for Eulerian nodes, xI = constant in time Points on the edges of elements behave similarly to the nodes: in two-dimensional Lagrangian meshes, element edges remain coincident with material lines, whereas in Eulerian meshes, the element edges remain fixed in space.
This is equivalent to the definition of engineering stress; however, no definition of the engineering stress is available in multi-dimensions. 9) A0 Therefore, if one of the stresses is known, the other can always be computed if the current and initial cross-sectional areas are known. â•‡ A constitutive equation, which describes material behavior and relates stress to a measure of deformation. In addition, we require the deformation to be continuous, which is often called a compatibility requirement.
The excitement in the 1960s was fueled by Ed Wilson’s liberal distribution of his first programs. The first generation of these programs had no name. In many laboratories throughout the world, engineers developed new applications by modifying and extending these early Introduction 5 codes developed at Berkeley; they had a tremendous impact on engineering and the subsequent development of finite element software. The second generation of linear programs developed at Berkeley were called SAP (Structural Analysis Program).