## 1 Introduction  
Sandwich beam and plate structures are widely used in aerospace, shipbuilding, construction and other industries due to their high specific stiffness and strength as well as their excellent energy absorption capability. The low weight penalty is especially of vital importance in the design of flight vehicles. Therefore, sandwich structures have received great attention [1]. In practice, the most widely used sandwich beam and plate structures are the sandwich structure having homogeneous face sheets and homogeneous core [2, 3]. The face sheets provide the primary load carrying capability, while the core serves to transfer the load between the face sheets. If the core is soft, its deformation effect on the mechanical behavior of the sandwich panel cannot be neglected. Besides, with the development of modern technologies, other types of sandwich structures, which have homogeneous face sheets and non-homogeneous core [4, 5] or non-homogeneous face sheets and homogeneous core, exist [6]. The reliability of the response predictions of sandwich structures is critically dependent on the accurate description and numerical simulations of the different phenomena associated with each of the aspects of material behavior [1]. It is found that most engineering theories of beams, plates and shells cannot recover all stresses (e.g., the transverse shear stress) accurately through their constitutive equations. A posteriori stress recovery technique proposed by [PERSON] et al. [6, 7] may recover the inaccurate stress components based on the accurate in-plane stress components. For simply supported sandwich panels with homogeneous face sheets and core and under sinusoidal loadings, the extended high-order sandwich panel theory (EHSAPT) [3] can yield very accurate stress distributions. In addition, for non-homogeneous core [8] or other loading and boundary conditions [9], the theory cannot recover all stresses accurately through its constitutive equations. A large variety of classical and advanced plate and shell theories are assessed by [PERSON] and [PERSON] [10; 11] to evaluate the bending response of sandwich plate and shell structures with soft cores. It is found that the error sources in the 2D modeling of sandwich plates and shells mainly come from the length-to-thickness-ratio (LTR) and the face-to-core-stiffness-ratio (FCSR). The FCSR error can only be contrasted by using the layerwise analysis [10]. Therefore, a new model where the soft-core is directly modeled by two-dimensional (2D) elasticity theory without a priori assumption [12] is proposed to ensure the accurate stress prediction. The top and bottom faces act like the elastic supports on the top and bottom edges of the core. This model has been proven to be appropriate for modeling the sandwich panels with a soft core [5; 12]. Since the solution domain is regular and thus both the differential quadrature method (DQM) and the harmonic differential quadrature method (HDQM) can be employed to solve the problem efficiently. The DQM, originated by [PERSON] and [PERSON] in 1971 [13], has been well developed since it was first introduced by [PERSON] et al. [14] for analyzing mechanical behavior of structural components. A variety of problems have been successfully solved thus far [15; 16], including beams and plates under point loads that are regarded as very challenging problems for point discrete methods [16; 17; 18; 19; 20; 21]. In the present investigation, the HDQM is employed. The HDQM was proposed by [PERSON] et al. [22]. Instead of polynomials used in the DQM, harmonic functions are used in the HDQM to determine the weighting coefficients. The Vandermonde matrix formed by using harmonic functions can be numerically inverted even when the number of points is greater than 15. This indicates that the HDQM is more stable than the DQM. To raise its computational efficiency, explicit formulas to compute the weighting coefficients directly are independently proposed by [PERSON] et al. [23] and [PERSON] et al. [24].