Cofactor Matrix | Definition, Calculation & Use

SOLVED: (10 marks)A 4-noded quadrilateral element is shown in Figure 1. The unit of the coordinates X and y is in mm. Determine the Jacobian matrix [J] for the element:4 (-1, 4)3 (4, 1)1 (-2, -1)2 (1, -1)Note: The shape functions for a 4-noded quadrilateral element in intrinsic coordinates are given by:N1 = (X-1)(4-y)/4, N2 = (1 X)(1-y)/4, N3 = (1 X)(1 y)/4, N4 = (1-X)(1 y)/4The Jacobian matrix [J] is defined as follows:[J] = [dx/dX, dx/dy] [dy/dX, dy/dy]Figure 1

SOLVED: Determine the Jacobian matrix [J] and its determinant for the elements shown in the figure below. Show that the determinant of [J] for rectangular and parallelogram shaped elements is equal to A=4, where A is the physical area of the element.3y(2, 3)(4, 3)(2, 1)(2, 1)2.1(2, 1) (2.(-2,(2, 1)(0, 0)(2, 0)

Construct the Jacobian matrix and compute its determinant:... | Filo