KEYWORDS: Convolution, Chemical elements, Particles, Lithium, 3D modeling, Computer architecture, Civil engineering, Numerical analysis, Finite element methods, Analytical research
A fourth-order accurate method is presented for the computation of dynamic response in the field of structural vibration.
Based on Benthien-Gurtin's principle of minimum transformed energy in linear elastodynamics in Laplace space,
functional in the form of single convolution integral is obtained by restoring the functional in the Laplace space back into
the original space. Based on the functional after spatial discretization, five-order Hermite interpolation functions are
adopted to approximate the nodal displacement in local time domain. A unconditionally stable two-step recursive method
is presented after the variational operation. The value of parameter θ is selected according to the unconditionally stable
analysis. Accuracy analyses and examples show that the algorithm is a higher accurate method. The method provided an
useful tool with simple code and easy implementation for the investigations of dynamic response computations in
practical engineering.
Quadrangular grid method is presented for simulating the propagation of elastic stress waves in two dimensional
orthotropic midia. The investigated lumps are constructed among the auxiliary quadrangular grids. The dynamic
equations of the investigated lump are given by integreting along the boundary of the investigated lump. The algorithm is
obtained by computing the nodal displacements and the central point stresses of the quadrangular grids alternately in
time domain. The numerical results are compared with the solutions of the finite element method. The results
demonstrate that the quadrangular grid method is of much higher calculational speed than the finite element method. The
stress wave propagation is simulated numerically in an orthotropic plate with a hole. Finally, stress wave propagation in
two layers of different media is studied and the example shows the features of the reflected and refracted wave
propagations.
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