Reference no: EM132631907

49325 CAMD Computer-Aided Mechanical Design

Question 1: As shown in Fig 1, a two-dimensional plate is discretised by only using one three-node triangular element, and the plate is loaded as follows.

Fig 1: A two-dimensional plate structure (1).

If element or global stiffness matrix [K] is given as follows

Calculate nodal displacements {U} of the element?

(2). If we have already known the strain-displacement matrix [B] and material property matrix [D]

(2.1) Calculate the strain {ε} and stress {σ} of the element.
(2.2) Calculate the strain {ε} and stress {σ} at point A within the element.

Question 2: As indicated in Fig 2, we assume that there is one quadrilateral element (No. 63) with 4 corner nodes (Q4) in the mesh. After finite element meshing and solution, the nodal coordinates, and displacements for the element No 63 in the global coordinate system are given in Table 1, respectively. Let the material Young's modulus E = 200GPa and Poisson's ratio µ = 0.3.

As shown in Fig 3, using the isoparametric Q4 element and 1-node Gaussian quadrature, calculate:
1. The strain {ε} of the element at the location (ξ=0, η=0).
2. The stress {σ} of the element at the location (ξ=0, η=0).

Fig 2: A structural mesh for a 2-D plan stress analysis problem

Table 1. Nodal coordinates and displacements for element No 63

Fig 3: Isoparametric element using 1-by-1 rule for Gaussian quadrature