Constant strain triangle

Solution of Posisson s equation Using a Constant Strain Triangle... 

In this section, we will proceed to develop a finite element formulation for the two-dimensional Poisson s equation using a linear displacement, constant strain triangle. Poisson s equation has many applications in polymer processing, such as injection and compression mold filling, die flow, potential problems, heat transfer, etc. The general form of Poisson s equation in two-dimensions is... 

The first step when formulating the finite element solution to the above equations, is to discretize the domain of interest into triangular elements, as schematically depicted in Fig. 9.13. In the constant strain triangles, represented in Fig. 9.14, the field variable within the element is approximated by,... 

Following the procedure used with the one-dimensional FEM model and using the constant strain triangle element developed in the previous section, we can now formulate the finite element equations for a transient conduction problem with internal heat generation rate per unit volume of Q. The governing equation is given by... 

Derive the equations that result in the element mass matrix for the constant strain triangle given in eqn. (9.72). 

Write a two-dimensional finite element program, using constant strain triangles and ID tube elements, to predict the flow and pressure distribution in a variable thickness die. Use the Hele-Shaw model. Compare the FEM results with the analytical solution for an end-fed sheeting die. 

Each block is modeled as linear, isotropic, homogeneous and elastic medium and subdivided with a mesh of constant-strain triangle finite-difference elements. Key factors affecting the hydraulic behaviour of fractures such as opening, closure, sliding and dilation of fractures are modeled by an elasto-perfectly plastic constitutive model of a fracture. A step-wise non-linear normal stress-normal closure relationship is adopted with a linear Mohr-Coulomb failure for shear (Figure 3). 

Figure 9.13 Finite element mesh using constant strain, or gradient, triangles for the domain presented in Fig. 9.12...

The behavior of LLDPE blends at constant rate of stretching, e, was examined at 150°C. The results are shown In Fig. 13 for Series I and II as well as in Fig. 14 for Series III. The solid lines In Fig. 13 represent 3n calc values computed from the frequency relaxation spectrtmi by means of Equation (36), while triangles Indicate the measured in steady state 3n values at y = 10 2 (s ), I.e. the solid lines and the points represent the predicted and measured linear viscoelastic behavior respectively. The agreement Is satisfactory. The broken lines In Fig. 13 represent the experimental values of the stress growth function In uniaxial extension, nE 3he distance between the solid and broken lines Is a measure of nonlinearity of the system caused by strain hardening, SH. 

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