Programming the Finite Element Method using C#

Define core classes for the finite element method in C#, such as STR node and STR line, and begin building a structure with a controller and local and global coordinates.

Define a public STR node class in C# with id, x, y, z properties, a constructor, and a toString method, integrating with STR core and STR support.

Continue building the finite element method in C# by adding the STR line class, defining nodes and properties, implementing a constructor and toString override, and debugging with a test run.

Build a fast internal vector helper in C# for finite element vector mathematics. Implement normalize, length, dot product, and cross product as static methods, with reference semantics.

Compute the line's length and center of gravity, derive local x, y, z unit vectors, and apply an epsilon tolerance to handle parallel to z cases in the refresh function.

Define a central STR controller as a single access point to the STR core, using internal constructors and a static current controller to centralize instantiation and support debugging.

Define a structure object to store nodes and lines for finite element method, enable binary serialization, and expose the SDR structure through the controller with initialization and toString reporting.

Define and manage structural materials within the controller, including automatic ID assignment, elastic modulus properties, and safe deletion to preserve line references.

Learn to define, modify, and delete STR releases in a c# controller, using springs to model end and start releases along a beam with x, y, z and torsional directions.

Implement supports in the finite element method with C#: rigid vs free springs, per-axis displacements and rotations, and an active flag, plus a controller to define, modify, and delete them.

Extend the finite element workflow in C# by implementing a section with area and inertias (Ix, Iy, Iz) and a controller to define, modify, and delete sections.

Define, modify, and delete nodes in the STR controller for the finite element method in C#, auto-assign IDs, and refresh lines or force delete them when coordinates or supports change.

Define, modify, and delete line elements in the finite element method using C sharp. Build lines from node pairs, assign ids, materials, sections, and releases, and implement null-safe reporting.

Explore the finite element method in c sharp by modeling loads with a base load class, including node, linear, and concentrated loads, equivalent loads, load cases, and load combinations.

Define load cases by adding a load case class with id, name, and type, using a global enum of dead, live, wind, and seismic loads for controller management.

Explore load combinations in C#, using inheritance from load cases, enum types, and lists of cases and factors; implement creation, modification, and deletion via a polymorphic controller.

Learn to implement base loads in the finite element method using c#, covering nodal and linear distributed loads, linear constraints, and a controller to add and delete loads.

Define a nodal load class in the finite element method using C#. Inherit from STR node and manage x, y, z forces.

Create a linear concentrated STR load on a bar with a relative location, enabling define, modify, and delete operations, and verify behavior through testing.

Define and implement a str node linear distributed load in a C# finite element framework, including start and end values, relative locations, reporting, and integration with the structure and controller.

This module introduces model generation for the finite element method using C Sharp, detailing intersection detection, line discretization into nodes, and separation of finite element bars from geometric lines.

Clear and prepare a structural finite element model in c#. Define backstage fem nodes and bars, discretize intersecting lines into elements, and solve f = kx with post-processing.

Prepare the structural model by detecting line intersections and creating autogenerated STR nodes at the intersection points, using line segments to simplify geometry and keep the controller tidy.

Determine line segment intersection in the finite element method with c#, by checking parallelism with cross products, computing the parametric intersection, and validating the intersection lies on both segments.

Generate FEM objects from structural nodes and from lines to build master and slave FEM nodes. Model supports as stiff springs between the nodes to allow future elastic behavior.

Explore how to generate master and slave finite element method nodes from supports in the finite element method using C#, linking them with springs, and preventing duplicate nodes.

Implement a duplicate-node check in the finite element method using c sharp, querying coordinates against existing str and fem nodes with an epsilon tolerance to prevent duplicates.

Convert str nodes and bars into fem nodes and elements, using springs to model pin, rigid, and free supports and releases, and generate extra nodes for spring elements.

Implement duplicate detection for fem bars by using a line finder and a bar searcher to check existing lines and reverse connections, ensuring a single bar per node pair.

Define a fem bar with two nodes, including vx, vy, vz, length, and its corresponding line, material, and section, while preparing infrastructure for higher order shape functions with three nodes.

Define a fem bar spring, implement its constructor, generate its id in the controller, set length and node connections, and add it to the structure bars.

Cycle through each str line, gather and sort the nodes from start to end, and discretize the line into fem bars, handling releases with a weak-spring connection.

Implement a C# method to find and sort all nodes on a line segment using a parametric t value for finite element analysis.

Convert line segment nodes to fem nodes, handle start and end releases with nodes and springs, and manage master and slave fem nodes in the finite element method using C#.

Discretize the line into fem bar beam elements between true nodes, distinguishing spring nodes, then define a Bernoulli beam class and implement the stiffness matrix in C#.

this lecture explains defining the fem bar beam as the main finite element, addressing node naming and constructor creation, and preparing to assemble the stiffness and force matrices for post-processing.

Learn to solve finite element method equations F = Kx by initializing matrices, assembling the global stiffness matrix, applying loads, and performing static condensation.

Initialize finite element matrices in C# with MathNet Numerics, building stiffness, load, and displacement matrices as sparse structures. Solve F = K X for load cases and store nodal displacements.

Calculate the global stiffness matrix by assembling local stiffness matrices with the transformation and initializing equivalent nodal loads. Use a base class with virtual methods for local stiffness.

Learn to assemble the global stiffness matrix from element matrices by mapping the six degrees of freedom per node into a sparse global matrix.

Compute the local stiffness matrix for a three-dimensional linear spring in C sharp and assemble a 60-by-60 sparse matrix using kx, ky, kz with uncoupled translational and rotational dofs.

Explore the principles of beam element local stiffness matrices in the finite element method, using C sharp to compare the easy 12×12 approach with a Galerkin shape function method.

Define a polynomial class in C# for the finite element method, enabling multiplication by numbers or polynomials, evaluation, derivation, and integration up to power 12 with a data loss caveat.

Define material properties, geometry, and beam shape functions to assemble the finite element stiffness matrix for a C sharp beam bar, using a get bar variables routine and pass-by-reference.

Compute the local stiffness matrix for beams using the Galerkin energy method with axial shape functions, deriving derivatives and integrating from 0 to L for axial, torsion, and bending.

Fill the global force matrix with nodal and distributed loads for linear static analysis, accumulate nodal forces using fem node positions, and preserve equivalent nodal forces for post-processing.

this lecture guides preparing equivalent nodal loads for linear concentrated and distributed forces in the finite element method with c sharp, covering bar selection and result storage.

Explain how to create a local equivalent nodal load matrix by transforming global nodal forces with a transformation matrix, store the results, and verify initialization during global stiffness matrix calculation.

Calculate equivalent nodal loads with the work equivalency method by converting global loads to local, computing local equivalents, then converting back to global via the 12×12 transformation matrix.

Compute equivalent nodal forces from bar concentrated loads in the finite element method using C#, transforming global loads to local with a transformation matrix.

Compute equivalent nodal loads for bar concentrated loads in the finite element method using C#. Transform global to local coordinates, and ensure the load lies on the bar before computing.

Learn to implement equivalent nodal loads from bar concentrated loads in a C# finite element method, deriving axial shape functions and computing Q1 and Q2.

Learn to compute equivalent nodal loads for bar distributed loads using the finite element method in C#, including linear distribution, trapezoidal integration, and transforming global inputs to local.

Implement equivalent nodal loads for bar distributed loads in C sharp by integrating piecewise load functions, constructing polynomial representations, and assembling shear, bending moment, and torsion terms.

Implement boundary conditions in the finite element method with C#, subdividing the stiffness matrix into supported and unsupported degrees of freedom using a boundary condition marker.

Apply static condensation to the finite element method in c sharp. Subdivide the stiffness matrix into K11, K12, K21, and K22 while handling boundary conditions.

Learn how to undo static condensation in the finite element method using C#, translating condensed results back into the global displacement and load matrices, handling boundary conditions.

Solve linear static equations in the finite element method using C#, applying the modal helper and static condensation to compute d1 and d2 from f1 and f2.

Store nodal displacements by transferring values from the global displacement matrix into each FEM node and corresponding STR node for post-processing and user output.

Continue building the finite element method in c#, implementing post-processing in the modal helper: initialize systems, calculate local and internal forces and displacements, and derive bending moment and shear diagrams.

Explore post-processing in the finite element method using c sharp by computing global displacements, transforming them to local displacements, and obtaining local forces via the local stiffness matrix.

Post-process beam diagrams by segmenting the range with line key points and computing internal moment, shear, and reactions at supports, mapping to global coordinates.

Define a line key point class in the finite element method using c#, capturing absolute location, internal and distributed forces, and load-case data for before and after states.

Explore implementing a cubic polynomial class in C# for finite element method post-processing, including constructors, operators for multiply and add, and methods to evaluate, integrate, and derive the polynomial.

Introduce line diagrams in the finite element method using C#, managed by a Diagram class that stores cubic equations with absolute locations, enabling add and clear operations.

Apply post processing in the finite element method using C# to compute internal forces and reactions. Iterate through structure nodes and bars and transform local forces to global.

Generate line key points for each fem bar by tracking cumulative distance and absolute locations. Update local and global loads, including concentrated and distributed cases, across load cases.

Generate line key points for linear distributed forces in the finite element method using C#. Convert distributed loads to local loads and place points at the start and end.

Generate and render line diagrams for finite element models in C#. Clear diagrams, iterate over load cases, compute deflection and rotation diagrams, and build internal force diagrams with shape functions.

Explore debugging a finite element program in C sharp with the STR core library, defining materials, sections, nodes, and loads, running analysis, and tackling null references and stack overflows.

Explore debugging and development of a finite element tool in C# using the STR core API, covering material and section definition, cantilever beam setup, load cases, and performing analysis.

Debugging a cantilever beam finite element model in C sharp, fix a line key point generation bug causing nan in diagrams, and improve post-processing to report analysis results and diagrams.

Implement cantilever beam benchmark analysis in the finite element method using C#, adding diagram evaluation and calculating critical values, absolute distances, and global maxima/minima after diagram generation.

Benchmark the finite element method in C#, building a 2D frame, applying loads, and analyzing shear force and moment diagrams, displacements, and reactions while debugging results.

Debug a 2D frame finite element method using C#, focusing on moment diagrams, line key points, and interpolating distributed loads to resolve errors.

Implement a 2d frame with an internal hinge in the finite element method using C#, including hinge releases and fixed supports, and analyze deflections, reactions, and moment diagrams.

Define a 3d frame in the finite element method using C#, run benchmarks, inspect results and deflections, and fix out-of-bounds issues to validate software accuracy.