The 'direct stiffness' global matrix after assembly is generally:
Choose the correct answer
Diagonal only — zero off-diagonal terms
Symmetric and banded (non-zeros near diagonal); singular until BCs applied — rigid body motion possible
Always upper triangular from assembly
Full dense matrix with all non-zero terms
Correct Answer
B. Symmetric and banded (non-zeros near diagonal); singular until BCs applied — rigid body motion possible
Why is this the answer?
Assembled global stiffness matrix [K]: (1) Symmetric: Kij = Kji (reciprocal theorem); (2) Banded: non-zero only near diagonal (elements near each other share DOF); (3) Singular before boundary conditions (rigid body modes possible); (4) Positive semi-definite. After applying boundary conditions (zeroing rows/columns of restrained DOF): becomes positive definite, non-singular → solvable. Bandwidth minimized by node numbering algorithms.
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