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+---
+type: concept
+title: "Axisymmetric Finite Elements"
+complexity: intermediate
+domain: computational-mechanics
+created: 2026-05-29
+updated: 2026-05-29
+address: c-000067
+aliases:
+  - axisymmetric element
+  - triangular torus element
+  - body of revolution finite element
+tags:
+  - concept
+  - finite-element-method
+  - continuum-elements
+  - axisymmetric-analysis
+status: current
+related:
+  - "[[Plane Stress and Plane Strain Elements]]"
+  - "[[Isoparametric Finite Elements]]"
+  - "[[Finite Element Thermal Stress Analysis]]"
+  - "[[Finite Element Modeling and Convergence Checks]]"
+sources:
+  - "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
+---
+
+# Axisymmetric Finite Elements
+
+## Definition
+
+Axisymmetric finite elements model bodies of revolution when the geometry, material behavior, boundary conditions, and loading are symmetric about an axis.
+
+## How They Work
+
+The simplest axisymmetric element is a triangular ring, or triangular torus, formed by rotating a triangular cross section around the axis of symmetry. The unknowns are radial and axial displacements in the cross section, but the strain state includes radial, axial, circumferential, and shear components.
+
+The stiffness and load terms include the circumferential integration effect, commonly appearing through a radius-weighted area integral. This lets a two-dimensional mesh represent a three-dimensional body of revolution such as a thick pressure vessel, circular footing problem, or axisymmetric solid.
+
+## Why It Matters
+
+Axisymmetric elements are efficient when their assumptions hold. They avoid the cost of a full 3D mesh while retaining the hoop strain and hoop stress behavior that plane stress or plane strain idealizations would miss.
+
+## Connections
+
+- [[Plane Stress and Plane Strain Elements]] are also 2D idealizations, but they do not represent circumferential strain.
+- [[Finite Element Thermal Stress Analysis]] includes an axisymmetric thermal strain case.
+- [[Isoparametric Finite Elements]] generalizes the same cross-section mapping idea to higher-order or quadrilateral axisymmetric elements.
+
+## Sources
+
+- [[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]
+