Rigid, a.
Etymology: [L. rigidus, fr. rigere to be stiff or numb: cf. F. rigide. Cf. Rigor. ]
1. Firm; stiff; unyielding; not pliant; not flexible. Upright beams innumerable Of rigid spears. Milton.
2. Hence, not lax or indulgent; severe; inflexible; strict; as, a rigid father or master; rigid discipline; rigid criticism; a rigid sentence. The more rigid order of principles in religion and government. Hawthorne.
Syn. -- Stiff; unpliant; inflexible; unyielding; strict; exact; severe; austere; stern; rigorous; unmitigated.
Shades of meaning
Fernald has no entry of its own for rigid; he lists it under severe.
Where he writes about it:
Rigid signifies primarily stiff, resisting any effort to change its shape; a corpse is said to be rigid in death; hence, in metaphorical sense, a rigid person or character is one that resists all efforts to change the will or course of conduct; a rigid rule or statement is one that admits of no deviation. — from severe
Rigorous is nearly akin to rigid, but is a stronger word, having reference to action or active qualities, as rigid does to state or character; a rigid rule may be rigorously enforced. — from severe
We speak of austere morality, rigid rules, rigorous discipline, stern commands, severe punishment, harsh speech or a harsh voice, hard requirements, strict injunctions, and strict obedience. — from severe