# 统计代写|主成分分析代写Principal Component Analysis代考|Creating Global Stiffness Matrix for 2D Truss Structure

In summary, the passage outlines the process of creating the global stiffness matrix for a two-dimensional truss structure using the direct stiffness method:

For each bar element in the truss, the local stiffness matrix is transformed into the global coordinate system using Equation 3.28 based on the orientation angle and geometric/material properties.

For the two-bar example from Figure 3.2, the transformed global stiffness matrices for elements 1 and 2 are given in matrix forms (3.33) and (3.34), respectively.

The connectivity of each element to the global nodes is established through Equations 3.35 and 3.36. This connectivity determines which entries of the global stiffness matrix are affected by each element’s stiffness terms.

To assemble the global stiffness matrix, the individual stiffness terms from each element matrix are allocated to their corresponding positions in the global matrix according to the connectivity table. Any zero entries imply that there is no connection and thus no stiffness contribution to that particular global degree of freedom.

The author illustrates how this allocation is done more efficiently by labeling the rows and columns of the element stiffness matrices with the corresponding global displacement indices (3.37 and 3.38).

Instead of including global displacement numbers within the element stiffness matrices for computation, a more practical approach involves defining an element-node connectivity table (Table 3.2) and an element displacement location vector (3.39), which simplifies the process of identifying where each element’s stiffness terms should be added to the global matrix.

For the truss example, the element displacement location vectors (3.40 and 3.41) specify which global displacements correspond to each row and column of the element stiffness matrices.

Once the element stiffness matrices are computed using the given geometric parameters, material properties, and the transformation formula (3.28), the global stiffness matrix is populated by systematically adding the element stiffness terms to their corresponding locations as identified by the element displacement location vectors.

By following this systematic assembly process, the global stiffness matrix is built up element-by-element until it represents the entire structure’s behavior under external loads. The final global stiffness matrix encapsulates the combined stiffness contributions of all elements and enables solving for the global displacement field when subjected to external loads.

### MATLAB代写

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