# 统计代写|主成分分析代写Principal Component Analysis代考|Finite Element Analysis for Truss Structures

This passage details the final steps in finite element analysis for a truss structure. After obtaining the global displacements through the solution process, one calculates the strain and stress within each element. The axial strain (ε(e)) for an element is derived from its nodal displacements converted to the element coordinate system using transformation matrices. The strain is then used to calculate the element axial stress (σ(e)) using Hooke’s Law (E * ε(e)).

For the truss example provided, given the modulus of elasticity (E1 = E2 = 10 × 10^6 lb/in.^2) and cross-sectional areas (A1 = A2 = 1.5 in.^2), the element stiffnesses (k1 and k2) are calculated. The global stiffness matrix is constructed accordingly and incorporates the known node constraints (U1 = U2 = U3 = U4 = 0).

With external loads applied, the global equilibrium equations are solved to find the displacements at node 3 (U5 and U6), which come out to be approximately 5.333 × 10^(-4) in. and 1.731 × 10^(-3) in. respectively. The reaction forces at nodes 1 and 2 are also calculated and verified to maintain equilibrium.

Next, the element displacements, stresses, and forces are individually computed for each element. For instance, for element 1, the element displacements are transformed from the global to the element coordinate system, and the element stress and nodal forces are then calculated using the derived element displacements and the known stiffness.

For element 2, the same procedure is followed, yielding its displacements, stress, and nodal forces. Both elements show tensile stress, signifying they are under tension.

Lastly, it is emphasized that while the finite element method provides a powerful tool for complex structural analyses, it is instructive to compare the results with simplified formulas when possible, such as computing the axial stress directly from force over area for axially loaded members. This comparison helps verify the accuracy of the finite element method solutions.

### MATLAB代写

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