During approach, the crew was advised of a windshear on final approach of +10 to -15 kts at 700 ft and 400 ft AGL. Winds were reported 170 degrees at 26 kts gusting to 40 kts. The pilot added 20 kts to his V-ref speed of 132 kts and selected auto-spoiler deployment. Prior to touchdown, the crew was advised again of a windshear alert in several quadrants. After touchdown, the aircraft bounced and the auto-spoilers deployed. The aircraft touched down again in what the crew described as a firm landing. The flight engineer found no apparent damage, so the crew did not write it up as a hard landing. On 12/31, damage was found on the upper crown of the fuselage between stations 660 and 680 from stringer S-10 left to S-10 right. Later inspections revealed nose gear damage also. Flight recorder read-out indicated that the approach speed varied from 143 to 170 kts with a touchdown speed of 163 kts. Significant windshear existed below 1,000 ft MSL and moderate to severe turbulence existed below 5,000 ft MSL. Updrafts and downdrafts existed below 100 ft AGL due to convergence/divergence of the winds.