RV-7 pilot reported a Class B airspace incursion resulted when altitude control was lost in convective activity.

Narrative

AC: Experimental RV-7APIC - Person A Flight Plan - None Direct to ZZZ VOR from ZZZ1Flight conditions: VFR; moderate Turbulence; DayWeather: Strong updrafts not forecast; no precipitation or Thunderstorms in the vicinity. contributing afternoon Heat over rising terrain.Phase of Flight: Enroute under Class B Altitude: climb to 7800ft under Class Bravo until clear and continue climbing 10;500 enroute.Contributing factors: Convective turbulence stronger than forecast. Rapid vertical air Movement exceeded ability to maintain altitude. Limited aircraft performance to interact climb during updraft.Event:While flying VFR climbing below Class at 7500 ft MSL approximately 15'NM southwest of ZZZ1; I encountered moderate turbulence. Without warning; a strong updraft caused the aircraft to climb despite application of nose-down pitch and reduced power. I also hit my head on the canopy even though I was buckled into a 5 point harness. The aircraft's climb rate briefly exceeded my ability to maintain altitude; and the aircraft climbed to approximately to 8;500 +'ft MSL; which was inside the ZZZ'B shelf (8;00 - 10;000). Due to hitting my head; I focused on maintaining level wings and allowing the aircraft to ride through the turbulence rather than attempting aggressive pitch inputs that could worsen control issues. I ended up at 9;200 ft MSL. To expedite exiting the Class'B shelf; I made a course change to the south; away from the Bravo boundary; while continuing to control power and I limited pitch to keep the safest control of the aircraft possible through the turbulence. Upon realizing the altitude deviation; I exited south keeping wings level with reduced power. Lessons Learned/Corrective Actions: Maintain a larger vertical buffer with Class B with convective activity is present.Consider requesting a Class B clearance in advance when operating near airspace boundaries in turbulence or unstable conditions especially hot afternoon over the surrounding area. Review forecasts for convective turbulence and vertical gust more thoroughly. Ensure Shoulder harness is secured tightly to minimize injury risk.When control authority in limited by turbulence/updrafts; prioritize attitude control and safe flight path rather than aggressive pitch changes.