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A Review of the Field Equations of Engineering
Concepts from Functional Analysis
Variational Formulations of BoundaryValue
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bilinear form boundary-value problem bounded Cauchy sequence coefficient matrix compute Consider constant continuous convergence coordinate defined deflection denotes derivatives differential equation domain dx dy dxl dx2 eigenvalue elastic energy essential boundary conditions exact solution Example existence and uniqueness finite-dimensional finite-element finite-element model finite-element solution given grad Hence Hilbert space Hm(Q inequality inner product space integral interpolation functions L2-norm Lagrange multiplier linear operator linear space linear subspace linear transformation linear vector space linearly independent mesh natural boundary conditions nodes normed space null space obtain operator equation orthogonal orthonormal parameter plate points Poisson equation polynomials positive-definite Prob real number rectangular element Ritz approximation Ritz method Ritz solution satisfy scalar shear shown in Fig Sobolev space solution of Eq solve stress tion transverse triangular element unique solution values variables variational formulation variational methods variational problem weak problem zero