Consider the thin (steel) 200 mm long tapered plate varying width from 40 mm to 5 mm along the length. Plate is fixed at the top. The plate has uniform thickness t = 1 mm, Young's modulus E = 200 x 10 Pa, and weight density p= 7800 kg/m. In addition to its self-weight, the plate is subjected to a point load P = 100 kg at its midpoint. (a) Model the plate with four finite elements. (b) Write down expressions for the element stiffness matrices and element body force vectors. (c) Assemble the structural stiffness matrix K and global load vector F. (d) solve for the global displacement vector Q. (e) Evaluate the stresses in each element. Differentiate between linear element and quadratic element. Derive the stiffness and force for two dimensional triangular elements.