Problem 2 A triangular element has three nodes with high order interpolation functions, which can be applicable for high strain rate. Develop the [D], [B], and [K] matrixes. Use the following quadratic displacement functions in x- and y-direction as interpolation functions: u(x, y) = α₁ + a2x + α3y² v(x, y) = a + α5x + α6y²

Two cables AB and AC are acting on the pole with forces FAB = 540N and FAC = 560N with parameters defining the attachment points shown in the table. We want to write the vector FAB in cartesian vector form. C X Y₂ parameters value units FAB 540 FAC 560 L ZI 3 7₂ 5.5 4 3.5 4 4 Submit Question N N m m m m m FAC A Y₁ Z write the vector FAB in Cartensian Vector Notation. Round your final answers to 3 significant figures. FAB= AB B L X1 N

The kinematic diagram is given as 012=60 degree and the speed of the mechanism is constant and 012=50 rad/sn in the slide mechanism whose limb dimensions are given below. Find the following items. AoA = r2 = 0.2 m A,Bo = r1 = 0.5 m 012 = 60° 12 = 50 rad/s %3D %3D A a) Write the vector closure equations b) Bring the vector closure equations into scalar form c) Find s13,014 d) Find s13,014 e) Find 513,014 S13 014 ri Bo 012 Ao

Two cables AB and AC are acting on the pole with forces FAB=540N and FAC = 560N with parameters defining the attachment points shown in the table. We want to write the vector AB in cartesian vector form. C Y₂ parameters value units 540 560 5.5 4 3.5 FAB FAC L Z1 Y 72 4 4 Submit Question N N m m m m m A x + 247.123 Y₁ write the vector FAB in Cartensian Vector Notation. Round your final answers to 3 significant figures. FAB= 282.427 Z B xj+-388.337 N

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In MATLAB write out a program to integrate the equations of motion of a rigid body. The inertia matrix is given by I = [125 0 0; 0 100 0; 0 0 75] which is a diagonal, where diag operator provides a matrix with given elements placed on its diagonal. Consider three cases where the body rotates 1 rad/sec about each principal axis. Integrate the resulting motion and study the angular rates and the resulting attitude (use any attitude coordinates). For each principal axis case, assume first that a pure spin about the principal axis is performed, and then repeat the simulation where a small 0.1 rad/sec motion is present about another principal axis. Discuss the stability of each motion. The code should produce a total of 6 simulations results when it is ran.

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Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three consecutive timesteps. 1.0- 0.8- 0.6- 0.4- 0.2 0.0- -0.2- -0.4- -0.6 T T T 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Figure 3: Advection equation, solution for three different timesteps. a) Provide an explanation what conditions and numerical setup could explain the curves. Identify which of the three curves is the first, second and third timestep.

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