Fig. 1

Schematic of triangular element in (a) global coordinate and (b) area coordinate (color online)"

Fig. 2

Schematic of (a) geometry model and (b) mesh of heat conduction in rectangular plate, where 302 elements with 182 nodes in total are created (color online)"

Fig. 3

Transient heat conduction in rectangular plate calculated with analytical method, present QSME method, and FEM: (a) temperature and (b) heat flux, where P1, P2, and P3 denote Point 1, Point 2, and Point 3, respectively (color online)"

Fig. 4

Maximum relative error logarithm emax of heat flux at probe 3 calculated with QSME method and FEM, compared with analytical results (color online)"

Fig. 5

Modeling of heat conduction in CFRP with elliptical hole (color online)"

Fig. 6

Mesh and temperature profiles in CFRP with elliptical defect: (a) Mesh 1 with 608 nodes, (b) Mesh 2 with 98 769 nodes, (c) QSME results based on Mesh 1, (d) FEM results based on Mesh 1, and (e) FEM results based on Mesh 2, considered as reference solutions (color online)"

Fig. 7

Comparison of heat flux in y direction along elliptical boundary clockwise from right endpoint (color online)"

Fig. 8

(a) Schematic of corrugated core sandwich plane structures and (b) aerodynamic heat loading curve versus time on top surface (color online)"

Fig. 9

Temperature distributions inside corrugated core sandwich plane structure: (a) mesh for QSME with 592 nodes and 684 elements, (b) temperature results by QSME, and (c) reference temperature results by FEM with 9 890 nodes and 16 661 elements (color online)"

Fig. 10

Maximum bottom surface temperature versus time (color online)"

Table B1

Points and weights for seven-point Hammer integration formula (α1 = 0.059 715 87, α2 = 0.797 426 99, β1 = 0.470 142 06, and β2 = 0.101 286 51)"

Table B2

Points and weights for six-point Gaussian quadrature"