--- title: "FEM steps and geometric modelling" subject: "Machine Design II" chapter: 1 key: "semester_7/machine_design_ii:fem-steps-geometric-modelling" source: https://www.bctengineer.com/q/semester_7/machine_design_ii/fem-steps-geometric-modelling site: BCT Engineering --- # FEM steps and geometric modelling Machine Design II · Chapter 1: Modeling and Simulation - Asked in: year not given, 4+4 marks - Video: [Understanding the Finite Element Method](https://www.youtube.com/watch?v=GHjopp47vvQ) — The Efficient Engineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/machine_design_ii/fem-steps-geometric-modelling - Whole chapter: https://www.bctengineer.com/md/semester_7/machine_design_ii/chapter-1 ## Question (a) Explain the steps of the finite element method for a structural analysis. (b) Differentiate between wireframe, surface and solid models used in computer generated geometric modelling. ## Short answer FEM steps: geometry creation, meshing, writing element equations (e.g., [k]=AE/L[[1,-1],[-1,1]]), assembly, applying boundary conditions and loads, solving for displacements, then postprocessing stresses. Wireframe stores only edges; surface models add bounding faces for hidden-line removal; solid models store complete volume, yielding mass properties and 3D element meshing. ## Answer #### (a) Steps of the finite element method The **finite element method (FEM)** divides a body into small elements joined at nodes, solves a simple equation on each element and assembles them to get the behaviour of the whole body. 1. **Preprocessing:** create the geometry, choose element type (bar, beam, triangle, quadrilateral, tetrahedron, brick), assign material properties ($E$, $\nu$) and section data. 2. **Discretisation (meshing):** divide the body into elements. Use a finer mesh where stress changes quickly (holes, fillets). 3. **Element equations:** for each element write $[k]^e\{u\}^e = \{f\}^e$ using shape functions. For a bar element: $[k]=\dfrac{AE}{L}\begin{bmatrix}1&-1\\-1&1\end{bmatrix}$. 4. **Assembly:** combine the element matrices into the global equation $[K]\{U\}=\{F\}$. 5. **Boundary conditions and loads:** fix the supports and apply forces. 6. **Solution:** solve for nodal displacements $\{U\}$. 7. **Postprocessing:** calculate strains, stresses and reactions, plot contours, and check convergence by refining the mesh. ```text Geometry -> Mesh -> Element k -> Assemble K -> Apply loads/supports -> Solve U -> Stress, strain -> Check, refine mesh ``` #### (b) Wireframe, surface and solid models | Point | Wireframe | Surface | Solid | |---|---|---|---| | Stores | Edges (lines, arcs) and vertices only | Edges plus bounding surfaces | Complete volume with inside and outside | | Hidden lines | Cannot be removed automatically; ambiguous | Can be removed | Can be removed | | Mass properties | Not available | Not available | Volume, mass, centre of gravity, moment of inertia | | FEM meshing | Only line elements | Shell elements | Solid (brick/tetra) elements | | Methods | Points and lines | Lofts, sweeps, NURBS | CSG (Boolean union, difference, intersection) and B-rep | | Use | Simple layout, skeletons | Car bodies, aircraft skins, moulds | Machine parts, assemblies, interference check | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Where should a finer mesh be used in a finite element model? A. Where stress changes quickly, such as holes and fillets B. Where the body is far from the load C. Only at the supports D. Everywhere equally, never locally Answer: A. Stress gradients are steep near holes and fillets, so smaller elements are needed there for accuracy. (Key point: Mesh refinement) 2. What is done in the assembly step? A. Supports are fixed and forces are applied B. Element stiffness matrices are combined into the global equation [K]{U} = {F} C. Stresses are plotted as contours D. The geometry is divided into elements Answer: B. Assembly combines element matrices into the global system. Loads and supports come next, meshing comes before. (Key point: Assembly) 3. How is the accuracy of an FEM result checked in postprocessing? A. By increasing the Young's modulus B. By removing the boundary conditions C. By using only one large element D. By refining the mesh and checking that the results converge Answer: D. Convergence is checked by refining the mesh until stresses and displacements stop changing noticeably. (Key point: Postprocessing and convergence) 4. Which model type can give volume, mass, centre of gravity and moment of inertia? A. Wireframe B. Solid C. Surface D. None of them Answer: B. Only a solid model stores the complete volume, so mass properties are available. Wireframe and surface models do not give them. (Key point: Solid vs wireframe model) ## Related in Machine Design II - [Role and types of models in design](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Amodels-role-engineering-design) — Machine Design II, chapter 1 - [Six-speed machine tool gearbox design](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Amachine-tool-speed-ladder-gear) — Machine Design II, chapter 5 ## Related in other subjects - [Wireframe, surface and solid modelling compared](https://www.bctengineer.com/question.md?key=semester_4%2Fcomputer_aided_design%3Awireframe-surface-solid-modeling) — Computer Aided Design, chapter 2 - [Basic steps in finite element analysis](https://www.bctengineer.com/question.md?key=semester_8%2Fcomputational_techniques_in_civil_engineering%3Afem-basic-steps) — Computational Techniques in Civil Engineering, chapter 1 - [Steps and advantages of finite element method](https://www.bctengineer.com/question.md?key=semester_8%2Ffinite_element_method%3Afem-steps-advantages) — Finite Element Method, chapter 1 - [Mathematical modelling and applications of FEM](https://www.bctengineer.com/question.md?key=semester_8%2Ffinite_element_method%3Amathematical-modeling-fem-applications) — Finite Element Method, chapter 1