write a matlab code to solve the question to find the nodal displacement and reaction using matlab code. ( subject- finite element mthod)

[Dyuman Joshi]

What have you attempted yet?

[DGM]

A code:

d = [0 0.0625 0.125 0.0625 0]; % meters

[AYUSH]

Thanks a lot I also got how to do and solved it. I did in this way:--

% Research Project: Finite Element Analysis

% Step 1: Define Problem Parameters % --------------------------------

% Given data k = 20; % Stiffness of all springs in kN/m P = 5; % Applied force in kN

% Display Problem Parameters fprintf('Given Parameters:\n'); fprintf('Stiffness (k) = %d kN/m\n', k); fprintf('Applied Force (P) = %d kN\n', P);

% Step 2: Formulate the Global Stiffness Matrix (K) % -------------------------------------------------

% Given modified global stiffness matrix K = [k -k 0 0 0; -k 2*k -k 0 0; 0 -k 2*k -k 0; 0 0 -k 2*k -k; 0 0 0 -k k];

% Display Global Stiffness Matrix fprintf('\nGlobal Stiffness Matrix (K):\n'); disp(K);

% Step 3: Apply Boundary Conditions % ----------------------------------

% Boundary Conditions: u1 = u5 = 0

% Set rows and columns 1 and 5 to zero, and diagonal elements to 1 K(1,:) = 0; K(:,1) = 0; K(1,1) = 1; K(5,:) = 0; K(:,5) = 0; K(5,5) = 1;

% Display Modified Stiffness Matrix with Boundary Conditions Applied fprintf('\nModified Global Stiffness Matrix (K) with Boundary Conditions:\n'); disp(K);

% Step 4: Define the Load Vector (F) % ----------------------------------

% Load Vector: P = 5 kN applied at node 3 F = [0; 0; P; 0; 0];

% Display Load Vector fprintf('\nLoad Vector (F):\n'); disp(F);

% Step 5: Solve for Displacements (u) and Reactions (R) % -----------------------------------------------------

% Displacements (u) and Reactions (R) u = K\F; % Displacements R = K*u; % Reactions

% Display Displacements and Reactions fprintf('\nDisplacements (u):\n'); disp(u); fprintf('\nReactions (R):\n'); disp®;

% Conclusion fprintf('\nAnalysis Complete. Results obtained successfully.\n');

Answer 1

[AYUSH]

% Research Project: Finite Element Analysis

% Step 1: Define Problem Parameters % --------------------------------

% Given data k = 20; % Stiffness of all springs in kN/m P = 5; % Applied force in kN

% Display Problem Parameters fprintf('Given Parameters:\n'); fprintf('Stiffness (k) = %d kN/m\n', k); fprintf('Applied Force (P) = %d kN\n', P);

% Step 2: Formulate the Global Stiffness Matrix (K) % -------------------------------------------------

% Given modified global stiffness matrix K = [k -k 0 0 0; -k 2*k -k 0 0; 0 -k 2*k -k 0; 0 0 -k 2*k -k; 0 0 0 -k k];

% Display Global Stiffness Matrix fprintf('\nGlobal Stiffness Matrix (K):\n'); disp(K);

% Step 3: Apply Boundary Conditions % ----------------------------------

% Boundary Conditions: u1 = u5 = 0

% Set rows and columns 1 and 5 to zero, and diagonal elements to 1 K(1,:) = 0; K(:,1) = 0; K(1,1) = 1; K(5,:) = 0; K(:,5) = 0; K(5,5) = 1;

% Display Modified Stiffness Matrix with Boundary Conditions Applied fprintf('\nModified Global Stiffness Matrix (K) with Boundary Conditions:\n'); disp(K);

% Step 4: Define the Load Vector (F) % ----------------------------------

% Load Vector: P = 5 kN applied at node 3 F = [0; 0; P; 0; 0];

% Display Load Vector fprintf('\nLoad Vector (F):\n'); disp(F);

% Step 5: Solve for Displacements (u) and Reactions (R) % -----------------------------------------------------

% Displacements (u) and Reactions (R) u = K\F; % Displacements R = K*u; % Reactions

% Display Displacements and Reactions fprintf('\nDisplacements (u):\n'); disp(u); fprintf('\nReactions (R):\n'); disp®;

% Conclusion fprintf('\nAnalysis Complete. Results obtained successfully.\n');