Using vpasolve to specify the variables not to solve for, or returning a struct with all zero values

Background:

I am attempting to write code to implement finite element into a simple structure for an arbitrary number of nodes. I am implementing the principle equation (global stiffness matrix)*(vector of unknowns)=(vector of external loads)

https://en.wikipedia.org/wiki/Stiffness_matrix

I am solving for the trivial case of 3 nodes currently (bottom left, top left corner and top right) but need a generalised code. I can obtain the global stiffness matrix with no issues. I have had 2 unsuccessful attempts solving the unknowns and loads so far:

1: attempting to create all symbolic variables for fixed properties and symbolic vectors for loads and unknowns. I don't want vpasolve to attempt to solve for the constants (length, height, modulus, etc..) only for the value in the load vectors. I don't know how to explicitly state the variables when the symbolic vectors are of changing size.

This code does not work. neither does letting symvar determine my variables

    [sol,sol2]=vpasolve(global_matrix*unknowns_sym==loads_sym,[loads_sym, unknowns_sym],100);

Approach 2: assigning the values of all material properties and leaving only the unknown and load vectors as symbolic variables: I get a struct with all the variables however values are incorrect. As far as I can tell there are 9 equations and 9 unknowns.

 syms unknowns_sym loads_sym Rx Rm
unknowns_sym = sym('B', [total_nodes*3 1]);
unknowns_sym(1)=displacement;
unknowns_sym(2)=0;
unknowns_sym(7)=0;
unknowns_sym(9)=0;
loads_sym = sym('A', [total_nodes*3 1]);
loads_sym(2)=0;
loads_sym(3)=0;
loads_sym(4)=0;
loads_sym(5)=0;
loads_sym(6)=0;
loads_sym(7)=Rx;
loads_sym(8)=0;
loads_sym(8)=Rm;
sol=vpasolve(global_matrix*unknowns_sym==loads_sym,100);

entire m file is attached

is there some way i am misusing vpasolve? is there a way to specify which variables NOT to solve for in solve/vpasolve?

is this solution of matrices this way a good approach?

the condition of the global matrix is infinite, so i suspect this could also be a cause of this error. (mathematically not sure if this is as expected for this matrix, but solutions via inverse of matrix division do not work, hence my smybolic attempt)

Answer 1

[Walter Roberson]

vpasolve() is only for numeric solutions. It uses a newton-type method if I recall. The number of variables being solved for must match the number of independent equations; numeric values are looked for that satisfy everything.