Abstract:
Although the Euler-Bernoulli beam element with block-diagonal mass matrix achieves superior frequency accuracy,its non-positive-definite property leads to noticeable numerical instability in transient finite element analysis.To resolve this issue,a boundary-enhanced lumped mass matrix is proposed in this study through introducing a stabilization term into the components of boundary entries of the block-diagonal mass matrix.It turns out that this boundary-enhanced lumped mass matrix guarantees the positive definiteness.Meanwhile,a frequency accuracy analysis based upon the perturbation theory indicates that the proposed boundary-enhanced lumped mass matrix yields a third-order accuracy for frequency computation,which is one order higher than that of the conventional lumped mass matrix with rotational inertia.Furthermore,an analytical eigenvalue analysis reveals that the critical time step corresponding to the boundary-enhanced lumped mass matrix is also larger compared with the conventional lumped mass matrix with rotational inertia,which enables a more efficient transient computation.Subsequently,the proposed boundary-enhanced lumped mass matrix is employed for the finite element analysis of vehicle-bridge interaction.Numerical results demonstrate that the proposed boundary-enhanced lumped mass matrix not only produces more favorable solution accuracy in comparison with the conventional lumped mass matrix with rotational inertia,but also effectively avoids the transient response divergence caused by the non-positive-definiteness of the block-diagonal mass matrix.Consequently,the proposed boundary-enhanced lumped mass matrix offers an efficient,accurate and stable way for the dynamic analysis for vehicle-bridge interaction.