ABSTRACT
Novel and more efficient numerical methods can be invented, only if we can always be open-minded. The traditional procedure of three steps used in displacement methods is very simple: (1) domain discretization, (2) displacement field construction (via shape function creation), and (3) weak formulation to derive the discretized algebraic equations system that can be solved using standard routines. The most popular finite element method (FEM) follows this process and its effectiveness has been proven [1,2]. To further advance, in meshfree methods we need to introduce an additional step after step 2: strain field construction, so as to separate steps 2 and 3, in order to create a room for improving significantly the solution accuracy, and for solving the compatibility issues in FEM so that incompatible methods can be formulated properly based on the weakened-weak (W2) formulation (see Chapter 5). Because techniques for strain field construction are relatively less developed, we are able
to introduce only a few techniques, and even for these few there are still many theoretical issues which need to be studied further. The author believes that the potential in this direction of development should not be underestimated, and hence a lot more efforts are needed. The success in this direction of development depends on two major issues: (1) the addition step of strain field construction should be simple, cost-effective, and without introducing addition degrees of freedom to the equations system; (2) it should show sufficient improvement with respect to FEM, and=or offer attractive properties. This chapter discusses some of the techniques used for strain field construction, which focus only on the works for weakened-weak formulations, including the so-called strainconstructed Galerkin (SC-Galerkin) formulations, which are discussed in Chapter 5.
