Triangular and tetrahedral space-time finite elements in vibration analysis

Recently, several methods of time integration of the equations of motion have been proposed. Many of them result in square mass, damping and stiffness matrices. The space–time finite element method is an extension of the FEM, familiar to most engineers, over the time domain. A special approach enables the use of triangular, tetrahedral and hyper-tetrahedral elements in time and space. By special division of the space–time layer the triangular matrix of coefficients in the system of equations can be obtained. A simple algorithm enables the storage of non-zero coefficients only. Dynamic solution requires a small amount of the memory compared to other methods, and ensures considerable reduction of arithmetic operations. The method presented is also efficient in solving both linear and non-linear problems. Matrices for a beam and plane stress/strain element are derived. Exemplary problems solved by the method described have proved the effectiveness of the application of triangular and tetrahedral space–time elements in vibration analysis.