User:Eml4500.f08.team.allen.oca/hw2-1

P. 8-1 In compact notation, the Global Force Displacement Equation is $$\left[K_{ij} \right]_{6x6} \left\{d_{j} \right\}_{6x1}=\left\{F_{i} \right\}_{6x1}$$ Here the $$\mathbf{K}$$ matrix is generally n by n. Note that a capital K is a global stiffness matrix and a lowercase k is a element stiffness matrix. $$\sum_{j=1}^{6}{k_{ij}d_{j}}=F_{i} $$ where i = 1,...,6 The Global Stiffness Matrix is $$\mathbf{K}_{nxn} = \left[k_{ij} \right]_{nxn}$$ The Global Displacement Matrix is $$\mathbf{d}_{nxn}=\left\{d_{j} \right\}_{nxn}$$ P. 8-2 Recall the Element Force Displacement rel. from P. 7-5 $$\mathbf{k}_{4x4}^{e}\mathbf{d}_{4x1}^{e}=\mathbf{f}_{4x1}^{e}$$ How would one go from element matrices (stiffness, displacement and force) to global matrices? The answer is through an assembly process: $$\bullet$$ Identify the correspondence between elements displacement dofs and global displacement dofs.