Structural Engineering & Statics
where the load goes
Concept

Bandwidth — where it appears

The largest difference between the node numbers at the two ends of any member, which fixes how far a stiffness matrix's non-zero entries stray from its diagonal. It is a property of the labelling rather than of the structure, and it decides the cost of a solution without affecting the answer at all.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

36 × 36210 non-zerosof 1296 entriesbandwidth 13nullity 3before the supports go indense solve 16kbanded 6ka member reaches only its own two nodes

The matrix that replaced the hand methods

Moment distribution passes moments round a frame until they stop moving. Virtual work computes one deflection at a time. Both are exact and both stop scaling in the low tens of members. What replaced them adds no physics at all — the whole of the invention is the bookkeeping.

deflection · stiffness method 0123four nodes, three freedoms eachthe marked member touches six of the twelvethe global matrix, twelve by twelvethirty-six entries added in; the rest untouched

The answer that depends on how it was divided

Every computed answer in this collection came out of a structure chopped into pieces — elements, strips, stations, trial positions. The chopping is invisible in the result and it is not neutral: some divisions give the exact answer, some give one that is always too stiff, and one of them changes nothing but the cost of getting there.

deflection · discretisation

Named alongside it

The objects these essays reach for when they reach for this one.

CompatibilityDegrees of freedomVirtual workCondition numberConvergenceDeterminacyDiscretisationEigenvalueEquilibriumFlexibilityFree bodyGlobal stiffness matrix

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