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Lecture: Structural analysis - Finite element

The Finite element approach is actually a numerical method for solving differential equations generated by theories of mechanics such as elasticity theory and strength of materials, depends heavily on the processing power of computers and is more applicable to structures of arbitrary size and complexity. | STRUCTURAL ANALYSIS FINITE ELEMENT 1 The Finite element approach: I is actually a numerical method for solving differential equations generated by theories of mechanics such as elasticity theory and strength of materials. depends heavily on the processing power of computers and is more applicable to structures of arbitrary size and complexity. an assembly of elements or components with various forms of connection between them. Thus, a continuous system such as a plate or shell is modeled as a discrete system with a finite number of elements interconnected at finite number of nodes. The behaviour of individual elements is characterised by the elements stiffness or flexibility relation, which altogether leads to the systems stiffness or flexibility relation. ` 2 we can use the mechanics of materials approach for simple one-dimensional bar elements, and the elasticity approach for more complex two- and three-dimensional elements. 3 Forms element two-dimensional: Three-dimensional: prismatic elements: one-dimensional tetrahedral element: most elements quadratic element cubic element most elements quadratic element cubic element most elements quadratic element cubic element most elements quadratic element cubic element 4 A program including: Read input data: -mechanical parameters of materials -the geometric parameters of the structure -network parameters conditions -load effects -pairing information elements -boundary conditions information element stiffness matrix K information element node force vector F determine the stiffness matrix K & vector force F impose boundary conditions (transformation matrix vector K & F) 5 solve simultaneous equations KQ = F (determining the overall node displacement vector Q) calculation of other quantities (calculation of stresses, deformation, strength test, etc.) results in: -in the results - Drawing diagrams, graphs 6 | STRUCTURAL ANALYSIS FINITE ELEMENT 1 The Finite element approach: I is actually a numerical method for solving differential equations generated by theories of mechanics such as elasticity theory and strength of materials. depends heavily on the processing power of computers and is more applicable to structures of arbitrary size and complexity. an assembly of elements or components with various forms of connection between them. Thus, a continuous system such as a plate or shell is modeled as a discrete system with a finite number of elements interconnected at finite number of nodes. The behaviour of individual elements is characterised by the elements stiffness or flexibility relation, which altogether leads to the systems stiffness or flexibility relation. ` 2 we can use the mechanics of materials approach for simple one-dimensional bar elements, and the elasticity approach for more complex two- and three-dimensional elements. 3 Forms element two-dimensional: Three-dimensional: .