MultiPhysicsVault/wiki/sources/A-First-Course-in-the-Finite-Element-Method.md

type, title, source_type, author, created, updated, address, aliases, tags, status, confidence, raw_path, source_files, related

type	title	source_type	author	created	updated	address	aliases	tags	status	confidence	raw_path	source_files	related
source	A First Course in the Finite Element Method	book	Daryl L. Logan	2026-05-29	2026-05-29	c-000061	A First Course in the Finite Element Method Logan FEM	source finite-element-method textbook structural-mechanics	current	high	.raw/AFirstCourseInTheFiniteElementMethod/	markdown_files image_files 84 4056	Daryl L. Logan Finite Element Method Direct Stiffness Method Bar and Truss Finite Elements Beam and Frame Finite Elements Plane Stress and Plane Strain Elements Axisymmetric Finite Elements Finite Element Load Vector Assembly Finite Element Modeling and Convergence Checks Finite Element Thermal Stress Analysis

A First Course in the Finite Element Method

Summary

This fourth-edition textbook by Daryl L. Logan presents the finite element method as an introductory engineering workflow. It starts with matrix notation and the general FEM steps, then builds from springs to bars, trusses, beams, frames, plane stress and strain elements, axisymmetric elements, isoparametric elements, three-dimensional stress analysis, plate bending, heat transfer, fluid flow, thermal stress, structural dynamics, and time-dependent heat transfer.

Contribution To This Wiki

Compared with Finite Element Procedures and Abaqus Theory Manual, this source is more pedagogical and element-by-element. It makes the standard displacement method concrete through worked structural elements before extending the same matrix assembly pattern to transport, thermal, and dynamic problems.

Extracted Threads

• Direct Stiffness Method - assembly of spring and structural element equations into K d = F.
• Bar and Truss Finite Elements - local bar stiffness, coordinate transformation, plane truss, and space truss analysis.
• Beam and Frame Finite Elements - Euler-Bernoulli and Timoshenko beam ideas, plane frames, grids, and spatial beam orientation.
• Plane Stress and Plane Strain Elements - CST and LST element development for two-dimensional stress analysis.
• Axisymmetric Finite Elements - triangular ring elements for bodies of revolution under axisymmetric loading.
• Finite Element Load Vector Assembly - equivalent nodal forces for distributed, body, surface, and thermal loads.
• Finite Element Modeling and Convergence Checks - mesh quality, symmetry, compatibility, equilibrium, stress interpretation, and convergence.
• Finite Element Thermal Stress Analysis - conversion of thermal strain into equivalent nodal force terms.

Source Structure

• Chapters 1-5: finite element steps, stiffness method, truss, beam, frame, grid, and substructure basics.
• Chapters 6-12: plane stress/strain, practical modeling, LST, axisymmetric elements, isoparametric formulation, 3D stress, and plate bending.
• Chapters 13-16: heat transfer, mass transport, fluid flow, thermal stress, structural dynamics, mass matrices, and transient heat transfer.
• Appendices: matrix algebra, linear equation solution, elasticity equations, equivalent nodal forces, virtual work, and selected structural properties.

Source Files

• Raw path: .raw/AFirstCourseInTheFiniteElementMethod/
• First file: .raw/AFirstCourseInTheFiniteElementMethod/AFirstCourseInTheFiniteElementMethod_001.md
• Composite hash: d5a513a540f36ea134f82d54205572834f6afee01f75c73a98dfc37c5b1389fd