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% ============== ASSUMING HOMOGENOUS PROPERTIES =================

% GENERATE ELEMENT MATRICES AND ASSYMBLE INTO SYSTEM

% Assemble n_d by n_d square matrix terms from n_e by n_e

for j = 1:n_e ; % loop over elements ====>> ====>> ====>> ====>>

S_e = zeros (n_i, n_i) ; M_e = zeros (n_i, n_i) ; % sys arrays

C_p = zeros (n_i, 1) ; C_e = zeros (n_i, 1) ; % sys arrays

s_L = zeros (n_i, n_i) ; m_L = zeros (n_i, n_i) ; % loc arrays

t_L = zeros (n_i, n_i) ; c_L = zeros (n_i, 1) ; % loc arrays

e_nodes = nodes (j, 1:n_n) ; % coectivity

% SET ELEMENT PROPERTIES & GEOMETRY

Option = 1 ; % select analysis case

[A, E, Line_e, Rho] = set_2D_truss_properties (n_n, Option) ;

%--> find member length and direction cosines

dx = x(e_nodes(2)) - x(e_nodes(1)) ; % x length

dy = y(e_nodes(2)) - y(e_nodes(1)) ; % y length

L_e = sqrt (dx * dx + dy * dy) ; % total length

cx = dx / L_e ; cy = dy / L_e ; % direction cosines

% ELEMENT CONDUCTION AND INTERNAL SOURCE MATRICES

% for q = 1:n_q ; % Loop over quadrature points ----> ---->

% Linear axial bar and cubic bending. DOF = u, v, u, v

% Form arrays in local axes, transform. 1 2 3 4

% stiffness

s_L = [ 1, 0, -1, 0 ;

0, 0, 0, 0 ;

-1, 0, 1, 0 ;

0, 0, 0, 0 ] * E * A / L_e ;

% Map line load to node forces ONLY

if ( any (Line_e) ) ; % then form forcing vector

fprintf ('WARNING: line loads not yet active. n')

end % if for set up line load nodal resultants

% Optional local mass matrix

if ( Rho > 0 )

m_L = [140, 0, 70, 0 ;

0, 0, 0, 0 ;

70, 0, 140, 0 ;

0, 0, 0, 0 ] * Rho * A * L_e ;

end % if mass requested

% end % for loop over n_q element quadrature points

% Define local to system DOF transformation matrix

t_L = [ cx cy 0 0 ; % (inverse t_L = transpose t_L)

-cy cx 0 0 ;

0 0 cx cy ; % joint 2

0 0 -cy cx ] ;

% Transform from local to system

S_e = t_L' * s_L * t_L ; M_e = t_L' * m_L * t_L ;

C_e = t_L' * c_L ;

% SCATTER TO (ASSEMBLE INTO) SYSTEM ARRAYS

% Insert completed element matrices into system matrices

[rows] = get_element_index (n_g, n_n, e_nodes); % eq numbers

S (rows, rows) = S (rows, rows) + S_e ; % add to system sq

C (rows) = C (rows) + C_e ; % add to sys column

end % for each j element in mesh

% ALLOCATE STORAGE FOR OPTIONAL REACTION RECOVERY

if ( EBC_count > 0 ) ; % reactions occur