Accurate representation of local effects due to concentrated and discontinuous loads in hybrid-Trefftz plate bending elements

Abstract

As opposed to conventional conforming elements, the assumed displacement field of a hybrid-Trefftz (HT) element must accurately satisfy the differential equilibrium conditions while the conformity is then imposed in a weighted residual sense. Unlike the homogeneous part of the element displacement field, the particular load-dependent part may be represented, in the case of a concentrated or a discontinuous load, by a suitable local solution extending either over the whole plate or confined to a patch of elements in the vicinity of the load. The main advantage of such an approach is that the FE mesh and, to a large extent, also the solution accuracy are independent of the load. The paper presents explicit expression of local solutions for a line load and a patch load which are of particular interest to plate bending analysis in the engineering practice. The accuracy and efficiency of the approach are assessed in a series of benchmark problems.